fbpx
Wikipedia

Gradshteyn and Ryzhik

May 05, 2024

Gradshteyn and Ryzhik (GR) is the informal name of a comprehensive table of integrals originally compiled by the Russian mathematicians I. S. Gradshteyn and I. M. Ryzhik. Its full title today is Table of Integrals, Series, and Products.

Table of Integrals, Series, and Products
Gradshteyn and Ryzhik, seventh English edition, 2007
AuthorRyzhik, Gradshteyn, Geronimus, Tseytlin et al.
CountryRussia
LanguageRussian, German, Polish, English, Japanese, Chinese
GenreMath
PublisherAcademic Press
Publication date
1943, 2015

Since its first publication in 1943, it was considerably expanded and it soon became a "classic" and highly regarded reference for mathematicians, scientists and engineers. After the deaths of the original authors, the work was maintained and further expanded by other editors.

At some stage a German and English dual-language translation became available, followed by Polish, English-only and Japanese versions. After several further editions, the Russian and German-English versions went out of print and have not been updated after the fall of the Iron Curtain, but the English version is still being actively maintained and refined by new editors, and it has recently been retranslated back into Russian as well.

Overview edit

One of the valuable characteristics of Gradshteyn and Ryzhik compared to similar compilations is that most listed integrals are referenced. The literature list contains 92 main entries and 140 additional entries (in the eighth English edition). The integrals are classified by numbers, which haven't changed from the fourth Russian up to the seventh English edition (the numbering in older editions as well as in the eighth English edition is not fully compatible). The book does not only contain the integrals, but also lists additional properties and related special functions. It also includes tables for integral transforms. Another advantage of Gradshteyn and Ryzhik compared to computer algebra systems is the fact that all special functions and constants used in the evaluation of the integrals are listed in a registry as well, thereby allowing reverse lookup of integrals based on special functions or constants.

On the downsides, Gradshteyn and Ryzhik has become known to contain a relatively high number of typographical errors even in newer editions, which has repeatedly led to the publication of extensive errata lists. Earlier English editions were also criticized for their poor translation of mathematical terms[1][2][3] and mediocre print quality.[1][2][4][5]

History edit

The work was originally compiled by the Russian mathematicians Iosif Moiseevich Ryzhik (Russian: Иосиф Моисеевич Рыжик, German: Jossif Moissejewitsch Ryschik)[6][nb 1] and Izrail Solomonovich Gradshteyn (Russian: Израиль Соломонович Градштейн, German: Israil Solomonowitsch Gradstein).[6][nb 2] While some contents were original, significant portions were collected from other previously existing integral tables like David Bierens de Haan's Nouvelles tables d'intégrales définies (1867),[6][7] Václav Jan Láska's Sammlung von Formeln der reinen und angewandten Mathematik (1888–1894)[6][8] or Edwin Plimpton Adams' and Richard Lionel Hippisley's Smithsonian Mathematical Formulae and Tables of Elliptic Functions (1922).[6][9]

The first edition, which contained about 5 000 formulas,[10][11][nb 3] was authored by Ryzhik,[nb 1] who had already published a book on special functions in 1936[6][12] and died during World War II around 1941.[6] Not announcing this fact, his compilation was published posthumously[6][nb 1] in 1943, followed by a second corrected edition in his name in 1948.[nb 4]

The third edition (1951) was worked on by Gradshteyn,[13] who also introduced the chapter numbering system in decimal notation. Gradshteyn planned considerable expansion for the fourth edition, a work he could not finish due to his own death.[6][nb 2] Therefore, the fourth (1962/1963) and fifth (1971) editions were continued by Yuri Veniaminovich Geronimus (Russian: Юрий Вениаминович Геронимус, German: Juri Weniaminowitsch Geronimus)[6][nb 5] and Michail Yulyevich Tseytlin (Russian: Михаил Ю́льевич Цейтлин, German: Michael Juljewitsch Zeitlin).[nb 6] The fourth edition contained about 12 000 formulas already.[14][nb 3]

Based on the third Russian edition, the first German-English edition with 5 400 formulas[15][nb 3] was published in 1957 by the East-German Deutscher Verlag der Wissenschaften (DVW) with German translations by Christa[nb 7] and Lothar Berg[nb 8] and the English texts by Martin Strauss.[nb 9] In Zentralblatt für Mathematik Karl Prachar wrote:[16]

"Die sehr reichhaltigen Tafeln wurden nur aus dem Russischen ins Deutsche und Englische übersetzt."
(Translation: The very comprehensive tables were only translated into German and English language.)

In 1963, it was followed by the second edition, a reprint edition with a four-page inlet listing corrections compiled by Eldon Robert Hansen.

Derived from the 1963 edition, but considerably expanded and split into two volumes, the third German-English edition by Ludwig Boll[nb 10] was finally published by MIR Moscow in 1981 (with permission of DVW and distributed through Verlag Harri Deutsch in the Western world); it incorporated the material of the fifth Russian edition (1971) as well.[nb 11]

Pending this third German-English edition an English-only edition by Alan Jeffrey[nb 12] was published in 1965. Lacking a clear designation by itself it was variously known as first, third or fourth English edition, as it was based on the then-current fourth Russian edition. The formulas were photographically reproduced and the text translated. This still held true for the expanded fourth English edition in 1980, which added chapters 10 to 17.[17]

Both of these editions saw multiple print runs each incorporating newly found corrections. Starting with the third printing, updated table entries were marked by adding a small superscript number to the entry number indicating the corresponding print run ("3" etc.), a convention carried over into later editions by continuing to increase the superscript number as kind of a revision number (no longer directly corresponding with actual print runs).

The fifth edition (1994), which contained close to 20 000 formulas,[18][nb 3] was electronically reset[3] in preparation for a CD-ROM issue of the fifth edition (1996) and in anticipation of further editions. Since the sixth edition (2000), now corresponding with superscript number "10", Daniel Zwillinger[nb 13] started contributing as well. The last edition being edited by Jeffrey before his death[nb 12] was the seventh English edition published in 2007 (with superscript number "11").[19] This edition has been retranslated back into Russian as "seventh Russian edition" in 2011.[20][nb 11]

For the eighth edition (2014/2015, with superscript number "12") Zwillinger took over the role of the editor. He was assisted by Victor Hugo Moll.[21][nb 14] In order to make room for additional information without increasing the size of the book significantly, the former chapters 11 (on algebraic inequalities), chapters 13 to 16 (on matrices and related results, determinants, norms, ordinary differential equations) and chapter 18 (on z-transforms) worth about 50 pages in total were removed and some chapters renumbered (12 to 11, 17 to 12). This edition contains more than 10 000 entries.[21][nb 3]

Related projects edit

In 1995, Alan Jeffrey published his Handbook of Mathematical Formulas and Integrals.[22] It was partially based on the fifth English edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and meant as an companion, but written to be more accessible for students and practitioners.[22] It went through four editions up to 2008.[22][23][24][25] The fourth edition also took advantage of changes incorporated into the seventh English edition of Gradshteyn and Ryzhik.[25]

Inspired by a 1988 paper in which Ilan Vardi [de] proved several integrals in Gradshteyn and Ryzhik,[26] Victor Hugo Moll with George Boros started a project to prove all integrals listed in Gradshteyn and Ryzhik and add additional commentary and references.[27] In the foreword of the book Irresistible Integrals (2004), they wrote:[28]

It took a short time to realize that this task was monumental.

Nevertheless, the efforts have meanwhile resulted in about 900 entries from Gradshteyn and Ryzhik discussed in a series of more than 30 articles[29][30][31] of which papers 1 to 28[a] have been published in issues 14 to 26 of Scientia, Universidad Técnica Federico Santa María (UTFSM), between 2007 and 2015[60] and compiled into a two-volume book series Special Integrals of Gradshteyn and Ryzhik: the Proofs (2014–2015) already.[61][62]

Editions edit

Russian editions edit

  • Рыжик, И. М. (1943). Таблицы интегралов, сумм, рядов и произведений [Tables of integrals, sums, series and products] (in Russian) (1 ed.). Moscow: Gosudarstvennoe Izdatel'stvo Tehniko-Teoretičeskoj Literatury (Государственное издательство технико-теоретической литературы) (GITTL / ГИТТЛ) (Tehteoretizdat / Техтеоретиздат). LCCN ltf89006085. 400 pages.[10][63]
  • Рыжик, И. М. (1948). Таблицы интегралов, сумм, рядов и произведений (in Russian) (2 ed.). Moscow: Gosudarstvennoe Izdatel'stvo Tehniko-Teoretičeskoj Literatury (Государственное издательство технико-теоретической литературы) (GITTL / ГИТТЛ) (Tehteoretizdat / Техтеоретиздат). 400 pages.[11]
  • Рыжик, И. М.; Градштейн, И. С. (1951). Таблицы интегралов, сумм, рядов и произведений (in Russian) (3 ed.). Moscow: Gosudarstvennoe Izdatel'stvo Tehniko-Teoretičeskoj Literatury (Государственное издательство технико-теоретической литературы) (GITTL / ГИТТЛ) (Tehteoretizdat / Техтеоретиздат). LCCN 52034158. 464 pages (+ errata inlet).[63][64][65]
  • Градштейн, И. С.; Рыжик, И. М. (1963) [1962]. Геронимус, Ю. В.; Цейтлин, М. Ю́. (eds.). Tablitsy Integralov, Summ, Riadov I Proizvedenii Таблицы интегралов, сумм, рядов и произведений (in Russian) (4 ed.). Moscow: Gosudarstvennoe Izdatel'stvo Fiziko-Matematicheskoy Literatury (Государственное издательство физико-математической литературы) (Fizmatgiz / Физматгиз). LCCN 63027211. 1100 pages (+ 8 page errata inlet in later print runs).[14] Errata:[66]
  • Градштейн, И. С.; Рыжик, И. М. (1971). Геронимус, Ю. В.; Цейтлин, М. Ю́. (eds.). Таблицы интегралов, сумм, рядов и произведений (in Russian) (5 ed.). Nauka (Наука). LCCN 78876185. Dark brown fake-leather, 1108 pages.[nb 11]
  • Градштейн, И. С.; Рыжик, И. М.; Геронимус, Ю. В.; Цейтлин, М. Ю́. (2011). Jeffrey, Alan; Zwillinger, Daniel (eds.). Таблицы интегралов, ряда и продуктов [Table of Integrals, Series, and Products] (in Russian). Translated by Maximov, Vasily Vasilyevich [in Russian] (7 ed.). Saint-Petersburg, Russia: BHV (БХВ-Петербург). ISBN 978-5-9775-0360-0. GR:11. l+1182 pages.[20][nb 11]

German editions edit

Polish edition edit

English editions edit

Japanese edition edit

See also edit

Notes edit

  1. ^ [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]
  1. ^ a b c Iosif Moiseevich Ryzhik (Иосиф Моисеевич Рыжик)[6] (1918?–1941?). VIAF 15286520. GND 107340518, 1087809320.[1][2] (NB. Some sources identify him as a sergeant (сержантом) born in 1918, originally from Vitebsk (Витебска), who was drafted into the army in 1939 from Chkalovsk (Чкаловска), Orenburg (Оренбург), and got missing in December 1941. However, since a birth year 1918 would have made him a very young author (18), this could also have been a namesake. In the foreword of the first edition of the book, Ryzhik thanked three mathematicians of the Moscow Mathematical Society for their suggestions and advice: Vyacheslav Vassilievich Stepanov (Вячеслав Васильевич Степанов), Aleksei Ivanovich Markushevich (Алексей Иванович Маркушевич), and Ilya Nikolaevich Bronshtein (Илья Николаевич Бронштейн), suggesting that he must have been in some way associated with this group.)
  2. ^ a b Izrail Solomonovich Gradshteyn (Израиль Соломонович Градштейн) (1899, Odessa – 1958, Moscow). VIAF 20405466, VIAF 310677818, VIAF 270418384. ISNI 0000000116049405. GND 11526194X.
  3. ^ a b c d e Following the sources, this article distinguishes between the documented number of formulas and the number of entries.
  4. ^ The fact that Ryzhik's death was not announced before the third edition of the book in 1951 might indicate that his status was unclear for a number of years, or, in the case of the first edition, that typesetting had already started, but actual production of the book had to be delayed and was then finalized in his absence as a consequence of the war.
  5. ^ Yuri Veniaminovich Geronimus (Юрий Венеаминович Геронимус) (1923–2013), GND 131451812.
  6. ^ Michail Yulyevich Tseytlin (Михаил Ю́льевич Цейтлин), also as M. Yu. Ceitlin, Michael Juljewitsch Zeitlin, Michael Juljewitsch Zeitlein, Michael Juljewitsch Tseitlin, Mikhail Juljewitsch Tseitlin (?–).
  7. ^ Christa Berg née Jahncke (?–), GND 122341597 (this entry contains an incorrect birth year and some incorrectly associated books).
  8. ^ Lothar Berg (1930-07-28 to 2015-07-27), GND 117708054. [5]
  9. ^ Martin D. H. Strauss also as Martin D. H. Strauß (1907-03-18 Pillau, Baltijsk, Ostpreußen – 1978-05-17, East-Berlin, GDR), GND 139569200, German physicist and philosopher. [7][8][9][10]
  10. ^ Ludwig Boll (1911-12-10 Gaulsheim, Germany – 1984-12-02), GND 1068090308, German mathematician. [12][13]
  11. ^ a b c d The seventh Russian edition (2011) was named after the seventh English edition (2007), of which it was a retranslation. There was no sixth genuinely Russian edition. The English series of editions was originally (1965) based on the fourth Russian edition (1962/1963). It is unknown if any changes for the fifth Russian edition (1971) or the third German-English edition (1981), which did incorporate material from the fifth Russian edition, were reflected in any of the English editions in between (and thereby in the seventh Russian edition as well).
  12. ^ a b Alan Jeffrey (1929-07-16 to 2010-06-06), GND 113118120. [14][15][16]
  13. ^ Daniel "Dan" Ian Zwillinger (1957–), GND 172475694.
  14. ^ Victor Hugo Moll (1956–), GND 173099572.

References edit

  1. ^ a b c d Shanks, Daniel (October 1966). "Reviews and Descriptions of Tables and Books 85: Table of Integrals, Series, and Products by I. S. Gradshteyn, I. M. Ryzhik" (PDF). Mathematics of Computation (review). 20 (96): 616–617. doi:10.2307/2003554. JSTOR 2003554. RMT:85. Retrieved 2016-03-04.
  2. ^ a b c d Luke, Yudell Leo (January 1981). "Reviews and Descriptions of Tables and Books 5: I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 1980" (PDF). Mathematics of Computation (review). 36 (153): 310–314. doi:10.2307/2007757. JSTOR 2007757. MSC:7.95,7.100. Retrieved 2016-03-04.
  3. ^ a b c d Kölbig, Kurt Siegfried (January 1995). "Reviews and Descriptions of Tables and Books 1: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Alan Jeffrey, ed.), Academic Press, Boston, 1994" (PDF). Mathematics of Computation. 64 (209): 439–441. doi:10.2307/2153347. JSTOR 2153347. MSC:00A22,33-00,44-00,65-00. Retrieved 2016-03-03.
  4. ^ a b c d Wimp, Jet (April 1997). "Tables of Integrals, Series and Products By I. S. Gradshteyn and I. M. Ryzhik, edited by Alan Jeffrey". American Mathematical Monthly.
  5. ^ a b c d Wimp, Jet (October 1997) [1997-09-30]. Koepf, Wolfram (ed.). "2. Tables of Integrals, Series and Products By I. S. Gradshteyn and I. M. Ryzhik, edited by Alan Jeffrey" (PDF). Books and Journals: Reviews. Orthogonal Polynomials and Special Functions. Vol. 8, no. 1. SIAM Activity Group on Orthogonal Polynomials and Special Functions. pp. 13–16. (PDF) from the original on 2022-01-20. Retrieved 2022-01-23.
  6. ^ a b c d e f g h i j k Wolfram, Stephen (2005-10-08). "The History and Future of Special Functions". Wolfram Technology Conference, Festschrift for Oleg Marichev, in honor of his 60th birthday (speech, blog post). Champaign, IL, USA: Stephen Wolfram, LLC. The story behind Gradshteyn-Ryzhik. from the original on 2016-04-07. Retrieved 2016-04-06. […] In 1936 Iosif Moiseevich Ryzhik had a book entitled Special Functions published by the United Moscow-Leningrad Scientific-Technical Publisher. Ryzhik died in 1941, either during the siege of Leningrad, or fighting on the Russian front. In 1943, a table of formulas was published under Ryzhik's name by the Governmental Moscow-Leningrad Technical-Theoretical Publisher. The only thing the book seems to say about its origins is that it's responding to the shortage of books of formulas. It says that some integrals marked in it are original, but the others mostly come from three books—a French one from 1858, a German one from 1894, and an American one from 1922. It explains that effort went into the ordering of the integrals, and that some are simplified by using a new special function s equal to Gamma[x+y-1]/(Gamma[x]Gamma[y]). It then thanks three fairly prominent mathematicians from Moscow University. That's basically all we know about Ryzhik. […] Israil Solomonovitch Gradshteyn was born in 1899 in Odessa, and became a professor of mathematics at Moscow State University. But in 1948, he was fired as part of the Soviet attack on Jewish academics. To make money, he wanted to write a book. And so he decided to build on Ryzhik's tables. Apparently he never met Ryzhik. But he created a new edition, and by the third edition, the book was known as Gradshteyn-Ryzhik. […] Gradshteyn died of natural causes in Moscow in 1958. Though somehow there developed an urban legend that one of the authors of Gradshteyn-Ryzhik had been shot as a piece of anti-Semitism on the grounds that an error in their tables had caused an airplane crash. […] Meanwhile, starting around 1953, Yurii Geronimus, who had met Gradshteyn at Moscow State University, began helping with the editing of the tables, and actually added the appendices on special functions. Later on, several more people were involved. And when the tables were published in the West, there were arguments about royalties. But Geronimus [in 2005 was] still alive and well and living in Jerusalem, and Oleg phoned him […]
  7. ^ Bierens de Haan, David (1867). Nouvelles tables d'intégrales définies [New tables of definite integrals] (in French) (1 ed.). Leiden, Netherlands: P. Engels. Retrieved 2016-04-17. (NB. This book had a precursor in 1858 named Tables d'intégrales définies [18] (published by C. G. van der Post in Amsterdam) with supplement Supplément aux tables d'intégrales définies [19] in ca. 1864. Cited as BI (БХ) in GR.)
  8. ^ Láska, Václav Jan (1888–1894). Sammlung von Formeln der reinen und angewandten Mathematik [Compilation of formulae of pure and applied mathematics] (in German). Vol. 1–3 (1 ed.). Braunschweig, Germany: Friedrich Vieweg und Sohn [de]. OCLC 24624148. Retrieved 2016-04-17. (NB. The book writes the author's name as Wenzel Láska. Cited as LA (Ла) in GR.)
  9. ^ Adams, Edwin Plimpton; Hippisley, Richard Lionel (1922). Greenhill, Alfred George (ed.). Smithsonian Mathematical Formulae and Tables of Elliptic Functions. Smithsonian Miscellaneous Collections. Vol. 74 (1 ed.). Washington D.C., USA: Smithsonian Institution. Retrieved 2016-04-17. (NB. Cited as AD (А) in GR.)
  10. ^ a b Archibald, Raymond Clare (October 1945). "Recent Mathematical Tables 219: I. M. Ryzhik, Tablitsy Integralov, Summ, Riadov i Proizvedeniĭ, Leningrad, OGIZ, 1943" (PDF). Mathematical Tables and Other Aids to Computation (MTAG). 1 (12). American Mathematical Society: 442–443. RMT:219. Retrieved 2016-03-04.
  11. ^ a b Hahn, Wolfgang (1950-07-05). "Rydzik, I. M.: Tabellen für Integrale, Summen, Reihen und Produkte. 2. Aufl. Moskau, Leningrad: Staatsverlag für techn.-theor. Lit., 1948". Zentralblatt für Mathematik (review) (in German). 34 (1/3). Berlin, Germany: 70. Zbl 0034.07001. Retrieved 2016-02-16.
  12. ^ Stepanov, Vyacheslav Vassilievich (1936). Preface. Специальные функции: Собрание формул и вспомогательные таблицы [Special functions: A collection of formulas and an auxiliary table]. By Ryzhik, Iosif Moiseevich (in Russian) (1 ed.). Moscow / Leningrad: Объединенное научно-техническое издательство, ONTI. Гострансизд-во. Глав. ред. общетехнич. лит-ры и номографии. from the original on 2016-04-09. Retrieved 2016-04-09. (160 pages.)
  13. ^ Rosenfeld (Розенфельд), Boris Abramowitsch (Борис Абрамович) [in German] (2003). "Math.ru" Об Исааке Моисеевиче Ягломе [About Isaac Moiseevich Yaglom]. Мат. просвещение (Mat. enlightenment) (in Russian): 25–28. from the original on 2022-01-12. Retrieved 2022-01-12 – via math.ru. […] во время антисемитской кампании, известной как «борьба с космополитизмом», был уволен вместе с И.М. Гельфандом и И. С. Градштейном […] [during the antisemitic campaign known as the "fight against cosmopolitanism", he was fired along with I. M. Gelfand and I. S. Gradstein.]
  14. ^ a b Bruins, Evert Marie [in German] (1964-01-02). "Gradšteĭn, I. S., und I. M. Ryžik: Integral-, Summen-, Reihen- und Produkttafeln. (Tablicy integralov, summ, rjadov i proizvedeniĭ) 4. Aufl. überarb. unter Mitwirkung von Ju. V. Geronimus und M. Ju. Ceĭtlin. Moskau: Staatsverlag für physikalisch-mathematische Literatur, 1962". Zentralblatt für Mathematik (list) (in German). 103 (1): 38. Zbl 0103.03801. Retrieved 2016-02-16.
  15. ^ a b Wrench, Jr., John William (October 1960). "Reviews and Descriptions of Tables and Books 69: I. M. Ryshik & I. S. Gradstein, Summen-, Produkt- und Integral-Tafeln: Tables of Series, Products, and Integrals, VEB Deutscher Verlag der Wissenschaften, Berlin" (PDF). Mathematics of Computation. 14 (72): 381–382. doi:10.2307/2003905. JSTOR 2003905. RMT:69. (PDF) from the original on 2016-03-16. Retrieved 2016-03-16.
  16. ^ a b Prachar, Karl (1959-09-15). . Zentralblatt für Mathematik (review) (in German). 80 (2): 337–338. Zbl 0080.33703. Archived from the original on 2016-02-17. Retrieved 2016-02-12.
  17. ^ a b c Papp, Frank J. "Gradshteyn, I. S.; Ryzhik, I. M.: Tables of integrals, series, and products. Corr. and enl. ed. by Alan Jeffrey. Incorporating the 4th ed. by Yu. V. Geronimus and M. Yu. Tseytlin (M. Yu. Tsejtlin). Transl. from the Russian – New York – London – Toronto. Volumes 1, 2. German and English Transl". Zentralblatt für Mathematik und ihre Grenzgebiete (review). 521: 193. MR 0582453. Zbl 0521.33001. Retrieved 2016-02-16.
  18. ^ a b "Gradshteyn, I. S.; Ryzhik, I. M. Table of integrals, series, and products. Transl. from the Russian by Scripta Technica, Inc. 5th ed. Boston, MA: Academic Press, Inc. (1994)". Zentralblatt MATH. 1994. ISBN 9780122947551. Zbl 0918.65002. Retrieved 2016-02-16.
  19. ^ a b Gradshteyn, Izrail Solomonovich; Ryzhik, Iosif Moiseevich; Geronimus, Yuri Veniaminovich; Tseytlin, Michail Yulyevich (February 2007). Jeffrey, Alan; Zwillinger, Daniel (eds.). Table of Integrals, Series, and Products. Translated by Scripta Technica (7 ed.). Academic Press, Inc. ISBN 978-0-12-373637-6. MR 2360010. GR:11. Retrieved 2016-02-21. [20]
  20. ^ a b Таблицы интегралов, ряда и продуктов [Table of Integrals, Series, and Products] (PDF) (in Russian) (7 ed.). BHV (БХВ-Петербург). 2011. ISBN 978-5-9775-0360-0. (PDF) from the original on 2016-03-16. Retrieved 2016-03-16.
  21. ^ a b c Gradshteyn, Izrail Solomonovich; Ryzhik, Iosif Moiseevich; Geronimus, Yuri Veniaminovich; Tseytlin, Michail Yulyevich; Jeffrey, Alan (2015) [October 2014]. Zwillinger, Daniel; Moll, Victor Hugo (eds.). Table of Integrals, Series, and Products. Translated by Scripta Technica (8 ed.). Academic Press, Inc. ISBN 978-0-12-384933-5. GR:12. Retrieved 2016-02-21.
  22. ^ a b c Jeffrey, Alan (1995-01-01). Handbook of Mathematical Formulas and Integrals (1 ed.). Academic Press, Inc. ISBN 978-0-12-382580-3.
  23. ^ Jeffrey, Alan (2000-08-01). Handbook of Mathematical Formulas and Integrals (2 ed.). Academic Press, Inc. ISBN 978-0-12-382251-2.
  24. ^ Jeffrey, Alan (2004). Handbook of Mathematical Formulas and Integrals (3 ed.). Academic Press, Inc. (published 2003-11-21). ISBN 978-0-12-382256-7. from the original on 2022-01-01. Retrieved 2016-03-01.
  25. ^ a b Jeffrey, Alan; Dai, Hui-Hui (2008-02-01). Handbook of Mathematical Formulas and Integrals (4 ed.). Academic Press, Inc. ISBN 978-0-12-374288-9. Retrieved 2016-03-01. (NB. Contents of companion CD-ROM: [21] [22])
  26. ^ Vardi, Ilan (April 1988). "Integrals: An Introduction to Analytic Number Theory" (PDF). American Mathematical Monthly. 95 (4): 308–315. doi:10.2307/2323562. JSTOR 2323562. (PDF) from the original on 2016-03-15. Retrieved 2016-03-14. [23]
  27. ^ Moll, Victor Hugo (April 2010) [2009-08-30]. "Seized Opportunities" (PDF). Notices of the American Mathematical Society. 57 (4): 476–484. (PDF) from the original on 2016-04-08. Retrieved 2016-04-08. [24]
  28. ^ Boros, George; Moll, Victor Hugo (2006) [September 2004]. Irresistible Integrals. Symbolics, Analysis and Experiments in the Evaluation of Integrals (reprinted 1st ed.). Cambridge University Press (CUP). p. xi. ISBN 978-0-521-79186-1. Retrieved 2016-02-22. [25] [26] (NB. This edition contains many typographical errors.)
  29. ^ Moll, Victor Hugo; Vignat, Christophe. (PDF). Scientia. Series A: Mathematical Sciences. Archived from the original on 2016-03-13. Retrieved 2016-03-13.{{cite journal}}: CS1 maint: unfit URL (link) (NB. This paper discusses 19 GR entries: 1.14.2.1, 1.320, 2.18.1.9, 3.753.2, 3.771.8, 6.611, 7.341.1, 7.341.2, 7.342, 7.343.1, 7.344.1, 7.344.2, 7.346, 7.348, 7.349, 7.355.1, 7.355.2, 8.411.1, 8.921. [27])
  30. ^ a b Amdeberhan, Tewodros; Dixit, Atul; Guan, Xiao; Jiu, Lin; Kuznetsov, Alexey; Moll, Victor Hugo; Vignat, Christophe. (PDF). Scientia. Series A: Mathematical Sciences. Archived from the original on 2016-03-13. Retrieved 2016-03-13.{{cite journal}}: CS1 maint: unfit URL (link) (NB. This paper discusses 51 GR entries: 1.320.1, 1.320.3, 1.320.5, 1.320.7, 2.01.5, 2.01.6, 2.01.7, 2.01.8, 2.01.9, 2.01.10, 2.01.11, 2.01.12, 2.01.13, 2.01.14, 2.513.1, 2.513.2, 2.513.3, 2.513.4, 3.231.5, 3.274.2, 3.541.8, 3.611.3, 3.621.3, 3.621.4, 3.624.6, 3.631.16, 3.661.3, 3.661.4, 3.675.1, 3.675.2, 3.688.1, 3.721.1, 3.747.7, 3.761.4, 4.381.1, 4.381.2, 4.381.3, 4.381.4, 4.521.1, 6.671.7, 6.671.8, 7.244.1, 7.244.2, 7.531.1, 7.531.2, 8.230.1, 8.230.2, 8.361.7, 8.370, 8.910.2, 8.911.1. It also contains 1 errata for GR entry 3.541.8. [28])
  31. ^ Gonzalez, Ivan; Kohl, Karen T.; Moll, Victor Hugo (2014-06-13) [2014-03-19]. "Evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets" (PDF). Scientia. Series A: Mathematical Sciences. 25 (published 2014): 65–84. Retrieved 2016-03-13. (NB. This paper is also incorporated into volume II.)
  32. ^ a b Moll, Victor Hugo (2006-11-06) [2006-07-21]. (PDF). Scientia. Series A: Mathematical Sciences. 14 (published 2007): 1–6. Archived from the original (PDF) on 2017-02-02. Retrieved 2016-03-14. [29] (NB. This paper (from volume I) discusses 10 GR entries: 3.419.2, 3.419.3, 3.419.4, 3.419.5, 3.419.6, 4.232.3, 4.261.4, 4.262.3, 4.263.1, 4.264.3. )
  33. ^ Moll, Victor Hugo (2006-11-06) [2006-06-27]. "The integrals in Gradshteyn and Ryzhik. Part 2: Elementary logarithmic integrals" (PDF). Scientia. Series A: Mathematical Sciences. 14 (published 2007): 7–15. Retrieved 2016-03-14. [31] (NB. This paper (from volume I) discusses 5 GR entries: 4.231.1, 4.231.5, 4.231.6, 4.232.1, 4.232.2. [32])
  34. ^ Moll, Victor Hugo (2007-01-16) [2006-12-27]. "The integrals in Gradshteyn and Ryzhik. Part 3: Combinations of logarithms and exponentials" (PDF). Scientia. Series A: Mathematical Sciences. 15 (published 2007): 31–36. arXiv:0705.0175. Retrieved 2016-03-14. [33] (NB. This paper (from volume I) discusses 8 GR entries: 4.331.1, 4.335.1, 4.335.3, 4.352.1, 4.352.2, 4.352.3, 4.352.4, 4.353.2. [34])
  35. ^ Moll, Victor Hugo (2007-01-16) [2006-12-27]. "The integrals in Gradshteyn and Ryzhik. Part 4: The gamma function" (PDF). Scientia. Series A: Mathematical Sciences. 15 (published 2007): 37–46. arXiv:0705.0179. Retrieved 2016-03-14. [35] (NB. This paper (from volume I) discusses 44 GR entries: 3.324.2, 3.326.1, 3.326.2, 3.328, 3.351.3, 3.371, 3.381.4, 3.382.2, 3.434.1, 3.434.2, 3.461.2, 3.461.3, 3.462.9, 3.471.3, 3.478.1, 3.478.2, 3.481.1, 3.481.2, 4.215.1, 4.215.2, 4.215.3, 4.215.4, 4.229.1, 4.229.3, 4.229.4, 4.269.3, 4.272.5, 4.272.6, 4.272.7, 4.325.8, 4.325.11, 4.325.12,, 4.331.1 4.333, 4.335.1, 4.335.3, 4.355.1, 4.355.3, 4.355.4, 4.358.2, 4.358.3, 4.358.4, 4.369.1, 4.369.2. [36])
  36. ^ Amdeberhan, Tewodros; Medina, Luis A.; Moll, Victor Hugo (2007-01-16) [2006-12-27]. "The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals" (PDF). Scientia. Series A: Mathematical Sciences. 15 (published 2007): 47–60. arXiv:0705.2379. Retrieved 2016-03-14. [37] [38] (NB. This paper (from volume I) discusses 10 GR entries: 3.621.1, 3.621.3, 3.621.4, 3.761.11, 3.764.1, 3.764.2, 3.821.3, 3.821.14, 3.822.1, 3.822.2. [39])
  37. ^ Moll, Victor Hugo (2007-10-31) [2007-08-31]. "The integrals in Gradshteyn and Ryzhik. Part 6: The beta function" (PDF). Scientia. Series A: Mathematical Sciences. 16 (published 2008): 9–24. arXiv:0707.2121. Retrieved 2016-03-14. [40] (NB. This paper (from volume I) discusses 65 GR entries: 3.191.1, 3.191.2, 3.191.3, 3.192.1, 3.192.2, 3.193, 3.194.3, 3.194.4, 3.194.6, 3.194.7, 3.196.2, 3.196.3, 3.196.4, 3.196.5, 3.216.1, 3.216.2, 3.217, 3.218, 3.221.1, 3.221.2, 3.222.2, 3.223.1, 3.223.2, 3.223.3, 3.224, 3.225.1, 3.225.2, 3.225.3, 3.226.1, 3.226.2, 3.241.2, 3.241.4, 3.241.5, 3.248.1, 3.248.2, 3.248.3, 3.249.1, 3.249.2, 3.249.5, 3.249.7, 3.249.8, 3.251.1, 3.251.2, 3.251.3, 3.251.4, 3.251.5, 3.251.6, 3.251.8, 3.251.9, 3.251.10, 3.251.11, 3.267.1, 3.267.2, 3.267.3, 3.311.3, 3.311.9, 3.312.1, 3.313.1, 3.313.2, 3.314, 3.457.3, 4.251.1, 4.273, 4.275.1, 4.321.1. [41])
  38. ^ Amdeberhan, Tewodros; Moll, Victor Hugo (2007-10-31) [2007-08-21]. "The integrals in Gradshteyn and Ryzhik. Part 7: Elementary examples" (PDF). Scientia. Series A: Mathematical Sciences. 16 (published 2008): 25–39. arXiv:0707.2122. Retrieved 2016-03-14. [42] (NB. This paper (from volume I) discusses 30 GR entries: 2.321.1, 2.321.2, 2.322.1, 2.322.2, 2.322.3, 2.322.4, 3.195, 3.248.4, 3.248.6, 3.249.1, 3.249.6, 3.252.1, 3.252.2, 3.252.3, 3.268.1, 3.310, 3.311.1, 3.351.1, 3.351.2, 3.351.7, 3.351.8, 3.351.9, 3.353.4, 3.411.19, 3.411.20, 3.471.1, 3.622.3, 3.622.4, 4.212.7, 4.222.1. [43])
  39. ^ Moll, Victor Hugo; Rosenberg, Jason; Straub, Armin; Whitworth, Pat (2007-10-31) [2007-08-31]. "The integrals in Gradshteyn and Ryzhik. Part 8: Combinations of powers, exponentials and logarithms" (PDF). Scientia. Series A: Mathematical Sciences. 16 (published 2008): 41–50. arXiv:0707.2123. Retrieved 2016-03-14. [44] (NB. This paper (from volume I) discusses 7 GR entries: 3.351.1, 4.331.1, 4.351.1, 4.351.2, 4.353.3, 4.362.1, 8.350.1. [45])
  40. ^ Amdeberhan, Tewodros; Moll, Victor Hugo; Rosenberg, Jason; Straub, Armin; Whitworth, Pat (2008-11-18) [2007-11-29]. "The integrals in Gradshteyn and Ryzhik. Part 9: Combinations of logarithms, rational and trigonometric functions" (PDF). Scientia. Series A: Mathematical Sciences. 17 (published 2009): 27–44. Retrieved 2016-03-14. [46] (NB. This paper (from volume I) discusses 45 GR entries: 2.148.4, 3.747.7, 4.223.1, 4.223.2, 4.224.1, 4.224.2, 4.224.3, 4.224.4, 4.224.5, 4.224.6, 4.225.1, 4.225.2, 4.227.1, 4.227.2, 4.227.3, 4.227.9, 4.227.10, 4.227.11, 4.227.13, 4.227.14, 4.227.15, 4.231.1, 4.231.2, 4.231.3, 4.231.4, 4.231.8, 4.231.9, 4.231.11, 4.231.12, 4.231.13, 4.231.14, 4.231.15, 4.231.19, 4.231.20, 4.233.1, 4.261.8, 4.291.1, 4.291.2, 4.295.5, 4.295.6, 4.295.11, 4.521.1, 4.531.1, 8.366.3, 8.380.3. [47])
  41. ^ a b c Medina, Luis A.; Moll, Victor Hugo (2008-11-18) [2007-11-29]. "The integrals in Gradshteyn and Ryzhik. Part 10: The digamma function" (PDF). Scientia. Series A: Mathematical Sciences. 17 (published 2009): 45–66. Retrieved 2016-03-14. [48] [49] (NB. This paper (from volume I) discusses 76 GR entries: 3.219, 3.231.1, 3.231.3, 3.231.5, 3.231.6, 3.233, 3.234.1, 3.235, 3.244.2, 3.244.3, 3.265, 3.268.2, 3.269.1, 3.269.3, 3.311.5, 3.311.6, 3.311.7, 3.311.8, 3.311.10, 3.311.11, 3.311.12, 3.312.2, 3.316, 3.317.1, 3.317.2, 3.427.1, 3.427.2, 3.429, 3.434.2, 3.435.3, 3.435.4, 3.442.3, 3.457.1, 3.463, 3.467, 3.469.2, 3.469.3, 3.471.14, 3.475.1, 3.475.2, 3.475.3, 3.476.1, 3.476.2, 4.241.1, 4.241.2, 4.241.3, 4.241.4, 4.241.5, 4.241.7, 4.241.8, 4.241.9, 4.241.10, 4.241.11, 4.243, 4.244.1, 4.244.2, 4.244.3, 4.245.1, 4.245.2, 4.246, 4.247.1, 4.247.2, 4.251.4, 4.253.1, 4.254.1, 4.254.6, 4.256, 4.271.15, 4.275.2, 4.281.1, 4.281.4, 4.281.5, 4.293.8, 4.293.13, 4.331.1, 8.371.2. [50])
  42. ^ Boyadzhiev, Khristo N.; Medina, Luis A.; Moll, Victor Hugo (2009-03-16) [2008-07-02]. "The integrals in Gradshteyn and Ryzhik. Part 11: The incomplete beta function" (PDF). Scientia. Series A: Mathematical Sciences. 18 (published 2009): 61–75. Retrieved 2016-03-14. [51] [52] (NB. This paper (from volume I) discusses 52 GR entries: 3.222.1, 3.231.2, 3.231.4, 3.241.1, 3.244.1, 3.249.4, 3.251.7, 3.269.2, 3.311.2, 3.311.13, 3.522.4, 3.541.6, 3.541.7, 3.541.8, 3.622.2, 3.623.2, 3.623.3, 3.624.1, 3.635.1, 3.651.1, 3.651.2, 3.656.1, 3.981.3, 4.231.1, 4.231.6, 4.231.11, 4.231.12, 4.231.14, 4.231.19, 4.231.20, 4.234.1, 4.234.2, 4.251.3, 4.254.4, 4.261.2, 4.261.6, 4.261.11, 4.262.1, 4.262.4, 4.263.2, 4.264.1, 4.265, 4.266.1, 4.271.1, 4.271.16, 8.361.7, 8.365.4, 8.366.3, 8.366.11, 8.366.12, 8.366.13, 8.370. [53])
  43. ^ Moll, Victor Hugo; Posey, Ronald A. (2009-03-16) [2008-07-02]. "The integrals in Gradshteyn and Ryzhik. Part 12: Some logarithmic integrals" (PDF). Scientia. Series A: Mathematical Sciences. 18 (published 2009): 77–84. Retrieved 2016-03-14. [54] (NB. This paper (from volume I) discusses 6 GR entries: 4.231.1, 4.233.1, 4.233.2, 4.233.3, 4.233.4, 4.261.8. [55])
  44. ^ Moll, Victor Hugo (2010-10-10) [2009-07-07]. "The integrals in Gradshteyn and Ryzhik. Part 13: Trigonometric forms of the beta function" (PDF). Scientia. Series A: Mathematical Sciences. 19 (published 2010): 91–96. arXiv:1004.2439. Retrieved 2016-03-14. [56] (NB. This paper (from volume I) discusses 21 GR entries: 3.621.1, 3.621.2, 3.621.3, 3.621.4, 3.621.5, 3.621.6, 3.621.7, 3.622.1, 3.623.1, 3.624.2, 3.624.3, 3.624.4, 3.624.5, 3.625.1, 3.625.2, 3.625.3, 3.625.4, 3.626.1, 3.626.2, 3.627, 3.628. [57])
  45. ^ a b c Amdeberhan, Tewodros; Moll, Victor Hugo (2010-10-10) [2009-07-07]. "The integrals in Gradshteyn and Ryzhik. Part 14: An elementary evaluation of entry 3.411.5" (PDF). Scientia. Series A: Mathematical Sciences. 19 (published 2010): 97–103. arXiv:1004.2440. Retrieved 2016-03-14. [58] (NB. This paper (from volume I) discusses 1 GR entry: 3.411.5. [59])
  46. ^ Albano, Matthew; Amdeberhan, Tewodros; Beyerstedt, Erin; Moll, Victor Hugo (2010-07-18) [2010-04-20]. "The integrals in Gradshteyn and Ryzhik. Part 15: Frullani integrals" (PDF). Scientia. Series A: Mathematical Sciences. 19 (published 2010): 113–119. arXiv:1005.2940. Retrieved 2016-03-14. [60] (NB. This paper (from volume I) discusses 12 GR entries: 3.232, 3.329, 3.412.1, 3.434.2, 3.436, 3.476.1, 3.484, 4.267.8, 4.297.7, 4.319.3, 4.324.2, 4.536.2. [61])
  47. ^ a b Boettner, Stefan Thomas; Moll, Victor Hugo (2010-07-21) [2010-03-22]. "The integrals in Gradshteyn and Ryzhik. Part 16: Complete elliptic integrals" (PDF). Scientia. Series A: Mathematical Sciences. 20 (published 2010): 45–59. arXiv:1005.2941. Retrieved 2016-03-14. [62] (NB. This paper (from volume II) discusses 36 GR entries: 1.421.1, 3.166.16, 3.166.18, 3.721.1, 3.821.7, 3.841.1, 3.841.2, 3.841.3, 3.841.4, 3.842.3, 3.842.4, 3.844.1, 3.844.2, 3.844.3, 3.844.4, 3.844.5, 3.844.6, 3.844.7, 3.844.8, 3.846.1, 3.846.2, 3.846.3, 3.846.4, 3.846.5, 3.846.6, 3.846.7, 3.846.8, 4.242.1, 4.395.1, 4.414.1, 4.432.1, 4.522.4, 4.522.5, 4.522.6, 4.522.7, 8.129.1. [63])
  48. ^ Amdeberhan, Tewodros; Boyadzhiev, Khristo N.; Moll, Victor Hugo (2010-07-21) [2010-03-22]. "The integrals in Gradshteyn and Ryzhik. Part 17: The Riemann zeta function" (PDF). Scientia. Series A: Mathematical Sciences. 20 (published 2010): 61–71. Retrieved 2016-03-14. [64] (NB. This paper (from volume II) discusses 36 GR entries: 3.333.1, 3.333.2, 3.411.1, 3.411.2, 3.411.3, 3.411.4, 3.411.6, 3.411.7, 3.411.8, 3.411.9, 3.411.10, 3.411.11, 3.411.12, 3.411.13, 3.411.14, 3.411.15, 3.411.17, 3.411.18, 3.411.21, 3.411.22, 3.411.25, 3.411.26, 4.231.1, 4.231.2, 4.261.12, 4.261.13, 4.262.1, 4.262.2, 4.262.5, 4.262.6, 4.264.1, 4.264.2, 4.266.1, 4.266.2, 4.271.1, 4.271.2. [65])
  49. ^ Koutschan, Christoph; Moll, Victor Hugo (2010-08-21) [2010-04-26]. "The integrals in Gradshteyn and Ryzhik. Part 18: Some automatic proofs" (PDF). Scientia. Series A: Mathematical Sciences. 20 (published 2010): 93–111. (PDF) from the original on 2016-03-14. Retrieved 2016-03-14. [66] [67] (NB. This paper (from volume II) discusses 7 GR entries: 2.148.3, 3.953, 4.535.1, 6.512.1, 7.322, 7.349, 7.512.5. [68])
  50. ^ Albano, Matthew; Amdeberhan, Tewodros; Beyerstedt, Erin; Moll, Victor Hugo (2011-04-13) [2010-12-23]. "The integrals in Gradshteyn and Ryzhik. Part 19: The error function" (PDF). Scientia. Series A: Mathematical Sciences. 21 (published 2011): 25–42. Retrieved 2016-03-14. [69] (NB. This paper (from volume II) discusses 42 GR entries: 3.321.1, 3.321.2, 3.321.3, 3.321.4, 3.321.5, 3.321.6, 3.321.7, 3.322.1, 3.322.2, 3.323.1, 3.323.2, 3.325, 3.361.1, 3.361.2, 3.361.3, 3.362.1, 3.362.2, 3.363.1, 3.363.2, 3.369, 3.382.4, 3.461.5, 3.462.5, 3.462.6, 3.462.7, 3.462.8, 3.464, 3.466.1, 3.466.2, 3.471.15, 3.471.16, 3.472.1, 6.281.1, 6.282.1, 6.283.1, 6.283.2, 6.294.1, 8.258.1, 8.258.2, 8.258.3, 8.258.4, 8.258.5. [70])
  51. ^ a b Kohl, Karen T.; Moll, Victor Hugo (2011-04-13) [2010-12-23]. "The integrals in Gradshteyn and Ryzhik. Part 20: Hypergeometric functions" (PDF). Scientia. Series A: Mathematical Sciences. 21 (published 2011): 43–54. Retrieved 2016-03-14. [71] (NB. This paper (from volume II) discusses 26 GR entries: 3.194.1, 3.194.2, 3.194.5, 3.196.1, 3.197.1, 3.197.2, 3.197.3, 3.197.4, 3.197.5, 3.197.6, 3.197.7, 3.197.8, 3.197.9, 3.197.10, 3.197.11, 3.197.12, 3.198, 3.199, 3.227.1, 3.254.1, 3.254.2, 3.259.2, 3.312.3, 3.389.1, 9.121.4, 9.131.1. [72])
  52. ^ Boyadzhiev, Khristo N.; Moll, Victor Hugo (2012-10-20) [2012-05-15]. "The integrals in Gradshteyn and Ryzhik. Part 21: Hyperbolic functions" (PDF). Scientia. Series A: Mathematical Sciences. 22 (published 2012): 109–127. (PDF) from the original on 2016-03-14. Retrieved 2016-03-14. (NB. This paper (from volume II) discusses 75 GR entries: 2.423.9, 3.231.2, 3.231.5, 3.265, 3.511.1, 3.511.2, 3.511.4, 3.511.5, 3.511.8, 3.512.1, 3.512.2, 3.521.1, 3.521.2, 3.522.3, 3.522.6, 3.522.8, 3.522.10, 3.523.2, 3.523.3, 3.523.4, 3.523.5, 3.523.6, 3.523.7, 3.523.8, 3.523.9, 3.523.10, 3.523.11, 3.523.12, 3.524.2, 3.524.4, 3.524.6, 3.524.8, 3.524.9, 3.524.10, 3.524.11, 3.524.12, 3.524.13, 3.524.14, 3.524.15, 3.524.16, 3.524.17, 3.524.18, 3.524.19, 3.524.20, 3.524.21, 3.524.22, 3.524.23, 3.525.1, 3.525.2, 3.525.3, 3.525.4, 3.525.5, 3.525.6, 3.525.7, 3.525.8, 3.527.1, 3.527.2, 3.527.3, 3.527.4, 3.527.5, 3.527.6, 3.527.7, 3.527.8, 3.527.9, 3.527.10, 3.527.11, 3.527.12, 3.527.13, 3.527.14, 3.527.15, 3.527.16, 3.543.2, 4.113.3, 4.231.12, 8.365.9. [73])
  53. ^ a b Glasser, Larry; Kohl, Karen T.; Koutschan, Christoph; Moll, Victor Hugo; Straub, Armin (2012-10-20) [2012-05-15]. "The integrals in Gradshteyn and Ryzhik. Part 22: Bessel-K functions" (PDF). Scientia. Series A: Mathematical Sciences. 22 (published 2012): 129–151. (PDF) from the original on 2016-03-14. Retrieved 2016-03-14. [74] (NB. This paper (from volume II) discusses 36 GR entries: 3.323.3, 3.324.1, 3.337.1, 3.364.3, 3.365.2, 3.366.2, 3.372, 3.383.3, 3.383.8, 3.387.1, 3.387.3, 3.387.6, 3.388.2, 3.389.4, 3.391, 3.395.1, 3.461.6, 3.461.7, 3.461.8, 3.461.9, 3.462.20, 3.462.21, 3.462.22, 3.462.23, 3.462.24, 3.462.25, 3.469.1, 3.471.4, 3.471.8, 3.471.9, 3.471.12, 3.478.4, 3.479.1, 3.547.2, 3.547.4, 8.432.6. [75])
  54. ^ Medina, Luis A.; Moll, Victor Hugo (2012-06-25) [2012-02-01]. "The integrals in Gradshteyn and Ryzhik. Part 23: Combination of logarithms and rational functions" (PDF). Scientia. Series A: Mathematical Sciences. 23 (published 2012): 1–18. Retrieved 2016-03-14. [76] [77] (NB. This paper (from volume II) discusses 54 GR entries: 3.417.1, 3.417.2, 4.212.7, 4.224.5, 4.224.6, 4.225.1, 4.225.2, 4.231.1, 4.231.2, 4.231.8, 4.231.9, 4.231.10, 4.231.11, 4.231.16, 4.231.17, 4.231.18, 4.233.1, 4.234.3, 4.234.6, 4.234.7, 4.234.8, 4.262.7, 4.262.8, 4.262.9, 4.291.1, 4.291.2, 4.291.3, 4.291.4, 4.291.5, 4.291.6, 4.291.7, 4.291.8, 4.291.9, 4.291.10, 4.291.11, 4.291.12, 4.291.13, 4.291.14, 4.291.15, 4.291.16, 4.291.17, 4.291.18, 4.291.19, 4.291.20, 4.291.21, 4.291.22, 4.291.23, 4.291.24, 4.291.25, 4.291.26, 4.291.27, 4.291.28, 4.291.29, 4.291.30. [78])
  55. ^ McInturff, Kim; Moll, Victor Hugo (2012-07-28) [2012-02-01]. "The integrals in Gradshteyn and Ryzhik. Part 24: Polylogarithm functions" (PDF). Scientia. Series A: Mathematical Sciences. 23 (published 2012): 45–51. Retrieved 2016-03-14. [79] (NB. This paper (from volume II) discusses 10 GR entries: 3.418.1, 3.514.1, 3.531.1, 3.531.2, 3.531.3, 3.531.4, 3.531.5, 3.531.6, 3.531.7, 9.513.1. [80])
  56. ^ Moll, Victor Hugo (2012-07-28) [2012-02-01]. "The integrals in Gradshteyn and Ryzhik. Part 25: Evaluation by series" (PDF). Scientia. Series A: Mathematical Sciences. 23 (published 2012): 53–65. Retrieved 2016-03-14. [81] (NB. This paper (from volume II) discusses 18 GR entries: 3.194.8, 3.311.4, 3.342, 3.451.1, 3.451.2, 3.466.3, 3.747.7, 4.221.1, 4.221.2, 4.221.3, 4.251.5, 4.251.6, 4.269.1, 4.269.2, 8.339.1, 8.339.2, 8.365.4, 8.366.3. [82])
  57. ^ a b Boyadzhiev, Khristo N.; Moll, Victor Hugo (2015-01-30) [2014-09-19]. "The integrals in Gradshteyn and Ryzhik. Part 26: The exponential integral" (PDF). Scientia. Series A: Mathematical Sciences. 26 (published 2015): 19–30. Retrieved 2016-03-14. [83] (NB. This paper (from volume II) discusses 41 GR entries: 3.327, 3.351.4, 3.351.5, 3.351.6, 3.352.1, 3.352.2, 3.352.3, 3.352.4, 3.352.5, 3.352.6, 3.353.1, 3.353.2, 3.353.3, 3.353.4, 3.353.5, 3.354.1, 3.354.2, 3.354.3, 3.354.4, 3.355.1, 3.355.2, 3.355.3, 3.355.4, 3.356.1, 3.356.2, 3.356.3, 3.356.4, 3.357.1, 3.357.2, 3.357.3, 3.357.4, 3.357.5, 3.357.6, 3.358.1, 3.358.2, 3.358.3, 3.358.4, 4.211.1, 4.211.2, 4.212.1, 4.212.2. [84])
  58. ^ Medina, Luis A.; Moll, Victor Hugo (2015-01-30) [2014-09-16]. "The integrals in Gradshteyn and Ryzhik. Part 27: More logarithmic examples" (PDF). Scientia. Series A: Mathematical Sciences. 26 (published 2015): 31–47. Retrieved 2016-03-14. [85] (NB. This paper (from volume II) discusses 37 GR entries: 3.194.3, 3.231.1, 3.231.5, 3.231.6, 3.241.3, 3.621.3, 3.621.5, 4.224.2, 4.231.1, 4.231.2, 4.231.8, 4.233.5, 4.234.4, 4.234.5, 4.235.1, 4.235.2, 4.235.3, 4.235.4, 4.241.5, 4.241.6, 4.241.7, 4.241.11, 4.251.1, 4.251.2, 4.252.1, 4.252.2, 4.252.3, 4.252.4, 4.254.2, 4.254.3, 4.255.2, 4.255.3, 4.257.1, 4.261.9, 4.261.15, 4.261.16, 4.297.8. [86])
  59. ^ a b Dixit, Atul; Moll, Victor Hugo (2015-02-01) [2014-09-30]. "The integrals in Gradshteyn and Ryzhik. Part 28: The confluent hypergeometric function and Whittaker functions" (PDF). Scientia. Series A: Mathematical Sciences. 26 (published 2015): 49–61. Retrieved 2016-03-14. [87] (NB. This paper (from volume II) discusses 17 GR entries: 7.612.1, 7.612.2, 7.621.1, 7.621.2, 7.621.3, 7.621.4, 7.621.5, 7.621.6, 7.621.7, 7.621.8, 7.621.9, 7.621.10, 7.621.11, 7.621.12, 8.334.2, 8.703, 9.211.4. [88])
  60. ^ Moll, Victor Hugo (2012). "Index of the papers in Revista Scientia with formulas from GR". Retrieved 2016-02-17.
  61. ^ Moll, Victor Hugo (2014-10-01). Special Integrals of Gradshteyn and Ryzhik: the Proofs. Monographs and Research Notes in Mathematics. Vol. I (1 ed.). Chapman and Hall/CRC Press/Taylor & Francis Group, LLC (published 2014-11-12). ISBN 978-1-4822-5651-2. Retrieved 2016-02-12. (NB. This volume compiles Scientia papers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 from issues 14 to 19.)
  62. ^ Moll, Victor Hugo (2015-08-24). Special Integrals of Gradshteyn and Ryzhik: the Proofs. Monographs and Research Notes in Mathematics. Vol. II (1 ed.). Chapman and Hall/CRC Press/Taylor & Francis Group, LLC (published 2015-10-27). ISBN 978-1-4822-5653-6. Retrieved 2016-02-12. (NB. This volume compiles 14 Scientia articles from issues 20, 21, 22, 23, 25 and 26 including papers 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28 and one unnumbered paper.)
  63. ^ a b "Ryžik, I. M.: Tafeln von Integralen, Summen, Reihen und Produkten. Moskau-Leningrad: Staatsverlag für technisch-theoretische Literatur, 1943". Zentralblatt für Mathematik (list) (in German). 60 (1): 123. 1957-04-01. Zbl 0060.12305. Retrieved 2016-02-16.
  64. ^ Prachar, Karl (1952-09-01). "Ryžik, I. M. und I. S. Gradštejn: Tafeln von Integralen, Summen, Reihen und Produkten. 3. umgearb. Aufl. Moskau-Leningrad: Staatsverlag für technisch-theoretische Literatur, 1951". Zentralblatt für Mathematik (review) (in German). 44 (1/5): 133. Zbl 0044.13303. Retrieved 2016-02-16.
  65. ^ a b Wrench, Jr., John William (October 1960). "Table Errata 293: I. M. Ryshik & I. S. Gradstein, Summen-, Produkt- und Integral-Tafeln: Tables of Series, Products, and Integrals, Deutscher Verlag der Wissenschaften, Berlin, 1957" (PDF). Mathematics of Computation. 14 (72): 401–403. JSTOR 2003934. MTE:293. (PDF) from the original on 2016-03-16. Retrieved 2016-03-16.
  66. ^ Градштейн, И. С.; Рыжик, И. М. (1971). "Errata in 4th edition". In Геронимус, Ю. В.; Цейтлин, М. Ю́. (eds.). Таблицы интегралов, сумм, рядов и произведений (in Russian) (5 ed.). Nauka (Наука). pp. 1101–1108. (NB. The 8-page errata list in later print runs of the fourth Russian edition affected 189 table entries.)
  67. ^ Ryshik-Gradstein: Summen-, Produkt- und Integral-Tafeln: Berichtigungen zur 1. Auflage (in German). Berlin, Germany: VEB Deutscher Verlag der Wissenschaften. 1962. MR 0175273. (NB. This brochure was available free of charge from the publisher on request.)
  68. ^ "Ryshik-Gradstein: Tafeln Summen Produkte Integrale: Berichtigungen zur 1. Auflage". L'Enseignement Mathématique. Bulletin Bibliographique: Livres Nouveaux (in French and German). 9: 5. 1963. Retrieved 2016-03-04. Die Berichtigung wird den Interessenten auf Anfrage kostenlos durch den Verlag geliefert.
  69. ^ Rodman, Richard B. (January 1963). "Table Errata 326: I. M. Ryshik & I. S. Gradstein, Summen-, Produkt- und Integral-Tafeln, Deutscher Verlag der Wissenschaften, Berlin, 1957" (PDF). Mathematics of Computation. 17 (81): 100–103. JSTOR 2003754. MTE:326. (PDF) from the original on 2016-03-16. Retrieved 2016-03-16. [89]
  70. ^ a b Schmieg, Glenn M. (July 1966). "Errata 392: I. M. Ryshik & I. S. Gradstein, Summen-, Produkt- und Integral-Tafeln: Tables of Series, Products, and Integrals, VEB Deutscher Verlag der Wissenschaften, Berlin, 1957" (PDF). Mathematics of Computation. 20 (95): 468–471. doi:10.2307/2003630. JSTOR 2003630. MTE:392. (PDF) from the original on 2016-03-16. Retrieved 2016-03-16.
  71. ^ Filliben, James J. [at Wikidata] (January 1970). "Table Errata 456: I. M. Ryshik & I. S. Gradstein, Summen-, Produkt- und Integral-Tafeln, VEB Deutscher Verlag der Wissenschaften, Berlin, 1957" (PDF). Mathematics of Computation. 24 (109): 239–242. JSTOR 2004912. MTE:456. (PDF) from the original on 2016-03-16. Retrieved 2016-03-16.
  72. ^ a b MacKinnon, Robert F. (January 1972). "Table Errata 486: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 26 (117): 305–307. doi:10.1090/s0025-5718-1972-0415970-6. JSTOR 2004754. MR 0415970. MTE:486. Retrieved 2016-03-04. [90]
  73. ^ "Gradshtejn, I. S.; Ryzhik, I. M.: Summen-, Produkt- und Integraltafeln. Band 1, 2. Deutsch und englisch. Übers. aus dem Russischen auf der Basis der 5. russ. Aufl., überarb. von J. Geronimus und M. Zeitlin. Tables of series, products, and integrals. Volumes 1, 2. German and English Transl". Zentralblatt für Mathematik und ihre Grenzgebiete (list) (in German). 448: 395. Zbl 0448.65002. Retrieved 2016-02-16.
  74. ^ "Gradshtejn, I. S.; Ryzhik, I. M.: Summen-, Produkt- und Integraltafeln. Band 1, 2. Deutsch und englisch. Übers. aus dem Russischen auf der Basis der 5. russ. Aufl., überarb. von J. Geronimus und M. Zeitlin. Tables of series, products, and integrals. Volumes 1, 2. German and English Transl". Zentralblatt für Mathematik und ihre Grenzgebiete (list) (in German). 456: 355. Zbl 0456.65001. Retrieved 2016-02-16.
  75. ^ Fettis, Henry E. (April 1967). "Table Errata 408: I. S. Gradshteyn & I. M. Ryzhik, Tables of Integrals, Series and Products, Fourth Edition, Academic Press, New York, 1965" (PDF). Mathematics of Computation. 21 (98): 293–295. JSTOR 2004214. MTE:408. Retrieved 2016-03-04.
  76. ^ Blake, J. R.; Wood, Van E.; Glasser, M. Lawrence; Fettis, Henry E.; Hansen, Eldon Robert; Patrick, Merrell R. (October 1968). "Table Errata 428: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, fourth edition, prepared by Yu. V. Geronimus & M. Yu. Tseytlin, Academic Press, New York, 1965" (PDF). Mathematics of Computation. 22 (104): 903–907. JSTOR 2004606. MR 0239122. MTE:428. Retrieved 2016-03-04. (NB. See 1972 corrigenda by Fettis and 1979 corrigenda by Anderson.)
  77. ^ Corrington, Murlan S.; Fettis, Henry E. (April 1969). "Table Errata 437: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 23 (106): 467–472. JSTOR 2004471. MR 0415966. Retrieved 2016-03-04. [91] [92]
  78. ^ Bradley, Lee C. (October 1969). "Table Errata 446: I. S. Gradshteyn & I. M. Ryzhik, Tables of Integrals, Series and Products, 4th edition, Academic Press, New York, 1965" (PDF). Mathematics of Computation. 23 (108): 891–892, s15–s17. doi:10.1090/s0025-5718-1969-0415968-8. JSTOR 2004993. MR 0415968. MTE:446. Retrieved 2016-03-04. [93]
  79. ^ Young, A. T. (January 1970). "Table Errata 451: A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Tables of Integral Transforms, McGraw-Hill Book Co., New York, 1954" (PDF). Mathematics of Computation. 24 (109): 239–242. doi:10.2307/2004614. JSTOR 2004912. MR 0257656. MTE:451. (PDF) from the original on 2016-03-16. Retrieved 2016-03-16. [94] (NB. The error also affects entry 3.252.10 on page 297 in GR.)
  80. ^ Muhlhausen, Carl W.; Konowalow, Daniel D. (January 1971). "Table Errata 473: I. S. Gradshteyn & I. M. Ryzhik, Tables of Integrals, Series and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 25 (113): 199–201. JSTOR 2005156. MR 0415969. MTE:473. Retrieved 2016-03-04. [95]
  81. ^ Nash, John C. (April 1972). "Table Errata 492: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 26 (118): 597–599. JSTOR 2005198. MR 0415971. MTE:492. Retrieved 2016-03-04. [96]
  82. ^ Fettis, Henry E. (April 1972). "Corrigendum: MTE 428, Math. Comp., v.22, 1968, pp. 903–907" (PDF). Mathematics of Computation. 26 (118): 601. doi:10.2307/2005199. JSTOR 2005199. MR 0415973. Retrieved 2016-03-04. [97] (NB. This corrigenda applies to MTE 428.)
  83. ^ Ojo, Akin; Sadiku, J. (April 1973). "Table Errata 503: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 27 (122): 451–452. doi:10.1090/s0025-5718-1973-0415972-0. JSTOR 2005649. MR 0415972. MTE:503. Retrieved 2016-03-04. [98] (NB. See 1982 corrigenda by Fettis.)
  84. ^ Fettis, Henry E. (April 1982). "Corrigenda: Ojo, Akin; Sadiku, J. (1973). Table Errata 503: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 38 (158): 657. doi:10.1090/S0025-5718-1982-0645681-X. JSTOR 2007312. MR 0645681. Retrieved 2016-03-14. (NB. This corrigenda applies to MTE 503.)
  85. ^ Scherzinger, Ann (October 1976). "Table Errata 528: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 30 (136): 899. doi:10.1090/s0025-5718-1976-0408192-x. JSTOR 2005420. MR 0408192. MTE:528. Retrieved 2016-03-04. [99]
  86. ^ Carr, Alistair R. (April 1977). "Table Errata 534: I. S. Gradshteyn & I. M. Ryzhik, Tables of Integrals, Series and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 31 (138): 614–616. doi:10.1090/s0025-5718-1977-0428676-9. JSTOR 2006446. MR 0428676. MTE:534. Retrieved 2016-03-04. [100]
  87. ^ Robinson, Neville I. (January 1978). "Table Errata 550: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 32 (141): 317–320. JSTOR 2006287. MR 0478539. MTE:550. Retrieved 2016-03-04. [101]
  88. ^ Fettis, Henry E. (January 1979). "Table Errata 557: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 33 (145): 430–431. JSTOR 2006060. MTE:557. Retrieved 2016-03-04.
  89. ^ Anderson, Michael (January 1979). "Corrigenda: p. 906 of MTE 428. I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 33 (145): 432–433. doi:10.2307/2006061. JSTOR 2006061. Retrieved 2016-03-04. (NB. This corrigenda applies to MTE 428.)
  90. ^ McGregor, John Ross (April 1979). "Table Errata 564: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 33 (146): 845–846. JSTOR 2006322. MTE:564. Retrieved 2016-03-04.
  91. ^ Birtwistle, David T. (October 1979). "Table Errata 565: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 33 (148): 1377. JSTOR 2006476. MTE:565. Retrieved 2016-03-04.
  92. ^ Gallas, Jason A. Carlson (October 1980). "Table Errata 572: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 35 (152): 1444. doi:10.1090/S0025-5718-1980-0583522-8. JSTOR 2006418. MR 0583522. MTE:572. Retrieved 2016-03-04. [102] [103]
  93. ^ Fettis, Henry E. (January 1981). "Table Errata 577: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 36 (153): 317–318. doi:10.1090/S0025-5718-1981-0595074-8. JSTOR 2007758. MR 0595074. MTE:577. Retrieved 2016-03-04.
  94. ^ Fettis, Henry E. (January 1981). "Table Errata 582: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 36 (153): 315–320. JSTOR 2007758. MR 0595074. MTE:582. (PDF) from the original on 2016-03-16. Retrieved 2016-03-04. (NB. See 1982 corrigenda by Fettis.)
  95. ^ Fettis, Henry E. (January 1982). "Corrigenda: Fettis, Henry E. (1981). Table Errata 582: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965" (PDF). Mathematics of Computation. 38 (157): 337. doi:10.1090/S0025-5718-1982-0637313-1. JSTOR 2007492. MR 0637313. (PDF) from the original on 2016-03-16. Retrieved 2016-03-16. (NB. This corrigenda applies to MTE 582.)
  96. ^ van Haeringen, Hendrik; Kok, Lambrecht P. [at Wikidata] (October 1982). "Table Errata 589: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, Corrected and enlarged edition, Academic Press, New York, First printing, 1980" (PDF). Mathematics of Computation. 39 (160): 747–757. doi:10.1090/S0025-5718-1982-0669666-2. JSTOR 2007357. MR 0669666. MTE:589. Retrieved 2016-02-22. [104] [105]
  97. ^ van Haeringen, Hendrik; Kok, Lambrecht P. [at Wikidata]. "I. S. Gradshteyn & I. M. Ryzhik, Tables of integrals, series, and products. Math. comput. 39, 747–757 (1982)". Zentralblatt für Mathematik und ihre Grenzgebiete (review). 521: 193. Zbl 0521.33002. Retrieved 2016-02-16.
  98. ^ Fettis, Henry E.; Deutsch, Emeric; Krupnikov, Ernst D. (October 1983). "Table Errata 601: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series and Products, Corrected and enlarged edition, Academic Press, New York, First Printing, 1980" (PDF). Mathematics of Computation. 41 (164): 780–783. doi:10.1090/S0025-5718-1983-0717727-2. JSTOR 2007718. MR 0717727. MTE:601. Retrieved 2016-03-04. [106]
  99. ^ Solt, György (October 1986). "Table Errata 607: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, corrected and enlarged edition prepared by A. Jeffrey, Academic Press, New York, 1980" (PDF). Mathematics of Computation. 47 (176): 767–768. doi:10.1090/S0025-5718-1986-0856719-2. JSTOR 2008202. MR 0856719. MTE:607. Retrieved 2016-03-03.
  100. ^ "Errors in the Integral Tables of Gradshteyn and Ryzhik with Correct Results from Mathematica". Mathematica Information Centre / Wolfram Library Archive: Technical Notes. Champaign, IL, USA: Wolfram Research, Inc. 2004 [2003]. from the original on 2003-04-25. Retrieved 2016-02-16.
  101. ^ "Errors in the Integral Tables of Gradshteyn and Ryzhik with Correct Results from Mathematica" (Technical note). Champaign, IL, USA: Wolfram Research, Inc. 2004 [2003]. from the original on 2004-06-19. Retrieved 2016-03-04.
  102. ^ "Table of integrals, series, and products. Ed. by Alan Jeffrey. CD-ROM version 1.0 for PC, MAC, and UNIX computers. 5th ed. (English) San Diego, CA: Academic Press (1996)". Zentralblatt MATH. 1996. ISBN 9780122947568. Zbl 0918.65001. Retrieved 2016-02-16.
  103. ^ Rosenblum, Marvin (October 1996). Koepf, Wolfram (ed.). "4. Table of Integrals, Series, and Products, CD-ROM Version 1.0 Edited by Alan Jeffrey" (PDF). Books and Journals: Review. Orthogonal Polynomials and Special Functions. Vol. 7, no. 1. SIAM Activity Group on Orthogonal Polynomials and Special Functions. pp. 11–12. (PDF) from the original on 2022-01-20. Retrieved 2022-01-23.
  104. ^ Kölbig, Kurt Siegfried (June 1996) [1995]. "Corrigenda: I. S. Gradshteyn & I. M. Ryzhik; Table of Integrals, Series, and Products, Fifth edition, Academic Press, Boston" (PDF). CERN Computing and Networks Division. CN/95/15. Retrieved 2016-02-12.
  105. ^ Kölbig, Kurt Siegfried (January 1995). "Table errata 617: I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Alan Jeffrey, ed.), Academic Press, Boston, 1994" (PDF). Mathematics of Computation. 64 (209): 449–460. doi:10.1090/S0025-5718-1995-1270626-0. JSTOR 2153354. MR 1270626. MTE:617. Retrieved 2016-03-03. [107]
  106. ^ Lambert, Adeline (January 1997). "Table Errata 628". Mathematics of Computation. 66 (217): 463. JSTOR 2153671. MR 1388890. MTE:628.
  107. ^ Fikioris, George (October 1998). "Table Errata 634". Mathematics of Computation. 67 (224): 1753–1754. JSTOR 2584882. MR 1625064. MTE:634. MSC:00A22,33-00,65-00.
  108. ^ Ruderman, Dan L. (2001-01-22). . Archived from the original on 2007-02-18. 3.381.3, 3.411.6, 3.721.3, 3.761.2, 3.761.9, 3.897.1, 6.561.13, 8.350.2
  109. ^ a b Rangarajan, Sarukkai Krishnamachari. "Gradshteyn, I. S.; Ryzhik, I. M. Table of integrals, series, and products. Translated from the Russian. Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. 6th ed. San Diego, CA: Academic Press". Zentralblatt MATH. ISBN 9780122947575. Zbl 0981.65001. Retrieved 2016-02-16.
  110. ^ "Table Errata 636". Mathematics of Computation. 71 (239): 1335–1336. July 2002. JSTOR 2698918. MTE:636.
  111. ^ "Table Errata 637". Mathematics of Computation. 71 (239): 1335–1336. July 2002. JSTOR 2698918. MTE:637.
  112. ^ Zwillinger, Daniel; Jeffrey, Alan (2005-11-10). "Errata for Tables of Integrals, Series, and Products, 6th edition by I. S. Gradshteyn and M. Ryzhik edited by Alan Jeffrey and Daniel Zwillinger, Academic Press, Orlando, Florida, 2000, ISBN 0-12-294757-6" (PDF). (PDF) from the original on 2016-03-08. Retrieved 2016-03-08. (NB. This list of 64 pages has 398 entries. According to Daniel Zwillinger it is incomplete.)
  113. ^ De Vos, Alexis (2020-11-09) [2009-03-19]. "Alexis De Vos". Universiteit Gent, Belgium. from the original on 2021-06-13. Retrieved 2022-01-12. […] Finally, he is the proud discoverer of an error in equation 3.454.1 of the Gradshteyn and Ryzhik "Tables of integrals, series, and products". See errata for 6th edition by Alan Jeffrey and Daniel Zwillinger, pages 1 and 19. The error is now corrected in the 7th edition page 363 (with acknowledgement in page xxvi). […]
  114. ^ "Gradshteyn, I. S.; Ryzhik, I. M. Table of integrals, series, and products. Translated from the Russian. Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. With one CD-ROM (Windows, Macintosh and UNIX). 7th ed. Amsterdam: Elsevier/Academic Press (ISBN 978-0-12-373637-6)". Zentralblatt MATH. ISBN 9780123736376. Zbl 1208.65001. Retrieved 2016-02-16.
  115. ^ Zwillinger, Daniel; Jeffrey, Alan (2008-04-11). "Errata for Tables of Integrals, Series, and Products (7th edition) by I. S. Gradshteyn and M. Ryzhik edited by Alan Jeffrey and Daniel Zwillinger, Academic Press, Orlando, Florida, 2007, ISBN 0-12-373637-4" (PDF). (PDF) from the original on 2016-03-08. Retrieved 2016-03-08. (NB. This list of 7 pages has 42 entries. According to Daniel Zwillinger it is incomplete.)
  116. ^ Veestraeten, Dirk (2015-07-24) [2015-06-21]. Written at Amsterdam, Netherlands. "Some remarks, generalizations and misprints in the integrals in Gradshteyn and Ryzhik". Scientia. Series A: Mathematical Sciences. 26. Valparaıso, Chile: Universidad Tecnica Federico Santa Marıa: 115–131. ISSN 0716-8446. S2CID 124124467. (PDF) from the original on 2021-12-26. Retrieved 2021-12-26. (18 pages)
  117. ^ Zwillinger, Daniel; Moll, Victor Hugo (2021-04-23) [2014-10-06]. "Errata for Tables of Integrals, Series, and Products (8th edition) by I. S. Gradshteyn and M. Ryzhik edited by Daniel Zwillinger and Victor Moll, Academic Press, 2014, ISBN 0-12-384933-0" (PDF) (6 ed.). (PDF) from the original on 2021-04-25. Retrieved 2021-12-26. (NB. This list of 33 pages has 191 entries.)

External links edit

  • Zwillinger, Daniel. "Gradshteyn and Ryzhik: Table of Integrals, Series, and Products (Home Page)". from the original on 2016-03-08. Retrieved 2016-03-08.
  • Moll, Victor Hugo. "List with the formulas and proofs in GR". from the original on 2010-01-09. Retrieved 2016-03-08.
  • "SCIENTIA, Series A: Mathematical Sciences – Official Journal of the Universidad Técnica Federico Santa María". Universidad Técnica Federico Santa María (UTFSM). Retrieved 2016-03-08.
  • Blackley, Jonathan "Seamus" (2021-06-12) [2021-06-11]. "One of my most cherished things, a tool so useful and powerful that I honesty have come to look at it as a friend: Table of Integrals, Series, and Products". twitter. from the original on 2021-09-11. Retrieved 2022-01-12.

May 05, 2024
gradshteyn, ryzhik, informal, name, comprehensive, table, integrals, originally, compiled, russian, mathematicians, gradshteyn, ryzhik, full, title, today, table, integrals, series, products, table, integrals, series, products, seventh, english, edition, 2007a. Gradshteyn and Ryzhik GR is the informal name of a comprehensive table of integrals originally compiled by the Russian mathematicians I S Gradshteyn and I M Ryzhik Its full title today is Table of Integrals Series and Products Table of Integrals Series and ProductsGradshteyn and Ryzhik seventh English edition 2007AuthorRyzhik Gradshteyn Geronimus Tseytlin et al CountryRussiaLanguageRussian German Polish English Japanese ChineseGenreMathPublisherAcademic PressPublication date1943 2015 Since its first publication in 1943 it was considerably expanded and it soon became a classic and highly regarded reference for mathematicians scientists and engineers After the deaths of the original authors the work was maintained and further expanded by other editors At some stage a German and English dual language translation became available followed by Polish English only and Japanese versions After several further editions the Russian and German English versions went out of print and have not been updated after the fall of the Iron Curtain but the English version is still being actively maintained and refined by new editors and it has recently been retranslated back into Russian as well Contents 1 Overview 2 History 3 Related projects 4 Editions 4 1 Russian editions 4 2 German editions 4 3 Polish edition 4 4 English editions 4 5 Japanese edition 5 See also 6 Notes 7 References 8 External linksOverview editOne of the valuable characteristics of Gradshteyn and Ryzhik compared to similar compilations is that most listed integrals are referenced The literature list contains 92 main entries and 140 additional entries in the eighth English edition The integrals are classified by numbers which haven t changed from the fourth Russian up to the seventh English edition the numbering in older editions as well as in the eighth English edition is not fully compatible The book does not only contain the integrals but also lists additional properties and related special functions It also includes tables for integral transforms Another advantage of Gradshteyn and Ryzhik compared to computer algebra systems is the fact that all special functions and constants used in the evaluation of the integrals are listed in a registry as well thereby allowing reverse lookup of integrals based on special functions or constants On the downsides Gradshteyn and Ryzhik has become known to contain a relatively high number of typographical errors even in newer editions which has repeatedly led to the publication of extensive errata lists Earlier English editions were also criticized for their poor translation of mathematical terms 1 2 3 and mediocre print quality 1 2 4 5 History editThe work was originally compiled by the Russian mathematicians Iosif Moiseevich Ryzhik Russian Iosif Moiseevich Ryzhik German Jossif Moissejewitsch Ryschik 6 nb 1 and Izrail Solomonovich Gradshteyn Russian Izrail Solomonovich Gradshtejn German Israil Solomonowitsch Gradstein 6 nb 2 While some contents were original significant portions were collected from other previously existing integral tables like David Bierens de Haan s Nouvelles tables d integrales definies 1867 6 7 Vaclav Jan Laska s Sammlung von Formeln der reinen und angewandten Mathematik 1888 1894 6 8 or Edwin Plimpton Adams and Richard Lionel Hippisley s Smithsonian Mathematical Formulae and Tables of Elliptic Functions 1922 6 9 The first edition which contained about 5 000 formulas 10 11 nb 3 was authored by Ryzhik nb 1 who had already published a book on special functions in 1936 6 12 and died during World War II around 1941 6 Not announcing this fact his compilation was published posthumously 6 nb 1 in 1943 followed by a second corrected edition in his name in 1948 nb 4 The third edition 1951 was worked on by Gradshteyn 13 who also introduced the chapter numbering system in decimal notation Gradshteyn planned considerable expansion for the fourth edition a work he could not finish due to his own death 6 nb 2 Therefore the fourth 1962 1963 and fifth 1971 editions were continued by Yuri Veniaminovich Geronimus Russian Yurij Veniaminovich Geronimus German Juri Weniaminowitsch Geronimus 6 nb 5 and Michail Yulyevich Tseytlin Russian Mihail Yu levich Cejtlin German Michael Juljewitsch Zeitlin nb 6 The fourth edition contained about 12 000 formulas already 14 nb 3 Based on the third Russian edition the first German English edition with 5 400 formulas 15 nb 3 was published in 1957 by the East German Deutscher Verlag der Wissenschaften DVW with German translations by Christa nb 7 and Lothar Berg nb 8 and the English texts by Martin Strauss nb 9 In Zentralblatt fur Mathematik Karl Prachar wrote 16 Die sehr reichhaltigen Tafeln wurden nur aus dem Russischen ins Deutsche und Englische ubersetzt Translation The very comprehensive tables were only translated into German and English language In 1963 it was followed by the second edition a reprint edition with a four page inlet listing corrections compiled by Eldon Robert Hansen Derived from the 1963 edition but considerably expanded and split into two volumes the third German English edition by Ludwig Boll nb 10 was finally published by MIR Moscow in 1981 with permission of DVW and distributed through Verlag Harri Deutsch in the Western world it incorporated the material of the fifth Russian edition 1971 as well nb 11 Pending this third German English edition an English only edition by Alan Jeffrey nb 12 was published in 1965 Lacking a clear designation by itself it was variously known as first third or fourth English edition as it was based on the then current fourth Russian edition The formulas were photographically reproduced and the text translated This still held true for the expanded fourth English edition in 1980 which added chapters 10 to 17 17 Both of these editions saw multiple print runs each incorporating newly found corrections Starting with the third printing updated table entries were marked by adding a small superscript number to the entry number indicating the corresponding print run 3 etc a convention carried over into later editions by continuing to increase the superscript number as kind of a revision number no longer directly corresponding with actual print runs The fifth edition 1994 which contained close to 20 000 formulas 18 nb 3 was electronically reset 3 in preparation for a CD ROM issue of the fifth edition 1996 and in anticipation of further editions Since the sixth edition 2000 now corresponding with superscript number 10 Daniel Zwillinger nb 13 started contributing as well The last edition being edited by Jeffrey before his death nb 12 was the seventh English edition published in 2007 with superscript number 11 19 This edition has been retranslated back into Russian as seventh Russian edition in 2011 20 nb 11 For the eighth edition 2014 2015 with superscript number 12 Zwillinger took over the role of the editor He was assisted by Victor Hugo Moll 21 nb 14 In order to make room for additional information without increasing the size of the book significantly the former chapters 11 on algebraic inequalities chapters 13 to 16 on matrices and related results determinants norms ordinary differential equations and chapter 18 on z transforms worth about 50 pages in total were removed and some chapters renumbered 12 to 11 17 to 12 This edition contains more than 10 000 entries 21 nb 3 Related projects editIn 1995 Alan Jeffrey published his Handbook of Mathematical Formulas and Integrals 22 It was partially based on the fifth English edition of Gradshteyn and Ryzhik s Table of Integrals Series and Products and meant as an companion but written to be more accessible for students and practitioners 22 It went through four editions up to 2008 22 23 24 25 The fourth edition also took advantage of changes incorporated into the seventh English edition of Gradshteyn and Ryzhik 25 Inspired by a 1988 paper in which Ilan Vardi de proved several integrals in Gradshteyn and Ryzhik 26 Victor Hugo Moll with George Boros started a project to prove all integrals listed in Gradshteyn and Ryzhik and add additional commentary and references 27 In the foreword of the book Irresistible Integrals 2004 they wrote 28 It took a short time to realize that this task was monumental Nevertheless the efforts have meanwhile resulted in about 900 entries from Gradshteyn and Ryzhik discussed in a series of more than 30 articles 29 30 31 of which papers 1 to 28 a have been published in issues 14 to 26 of Scientia Universidad Tecnica Federico Santa Maria UTFSM between 2007 and 2015 60 and compiled into a two volume book series Special Integrals of Gradshteyn and Ryzhik the Proofs 2014 2015 already 61 62 Editions editRussian editions edit Ryzhik I M 1943 Tablicy integralov summ ryadov i proizvedenij Tables of integrals sums series and products in Russian 1 ed Moscow Gosudarstvennoe Izdatel stvo Tehniko Teoreticeskoj Literatury Gosudarstvennoe izdatelstvo tehniko teoreticheskoj literatury GITTL GITTL Tehteoretizdat Tehteoretizdat LCCN ltf89006085 400 pages 10 63 Ryzhik I M 1948 Tablicy integralov summ ryadov i proizvedenij in Russian 2 ed Moscow Gosudarstvennoe Izdatel stvo Tehniko Teoreticeskoj Literatury Gosudarstvennoe izdatelstvo tehniko teoreticheskoj literatury GITTL GITTL Tehteoretizdat Tehteoretizdat 400 pages 11 Ryzhik I M Gradshtejn I S 1951 Tablicy integralov summ ryadov i proizvedenij in Russian 3 ed Moscow Gosudarstvennoe Izdatel stvo Tehniko Teoreticeskoj Literatury Gosudarstvennoe izdatelstvo tehniko teoreticheskoj literatury GITTL GITTL Tehteoretizdat Tehteoretizdat LCCN 52034158 464 pages errata inlet 63 64 65 Gradshtejn I S Ryzhik I M 1963 1962 Geronimus Yu V Cejtlin M Yu eds Tablitsy Integralov Summ Riadov I Proizvedenii Tablicy integralov summ ryadov i proizvedenij in Russian 4 ed Moscow Gosudarstvennoe Izdatel stvo Fiziko Matematicheskoy Literatury Gosudarstvennoe izdatelstvo fiziko matematicheskoj literatury Fizmatgiz Fizmatgiz LCCN 63027211 1100 pages 8 page errata inlet in later print runs 108 109 14 Errata 66 Gradshtejn I S Ryzhik I M 1971 Geronimus Yu V Cejtlin M Yu eds Tablicy integralov summ ryadov i proizvedenij in Russian 5 ed Nauka Nauka LCCN 78876185 Dark brown fake leather 1108 pages nb 11 Gradshtejn I S Ryzhik I M Geronimus Yu V Cejtlin M Yu 2011 Jeffrey Alan Zwillinger Daniel eds Tablicy integralov ryada i produktov Table of Integrals Series and Products in Russian Translated by Maximov Vasily Vasilyevich in Russian 7 ed Saint Petersburg Russia BHV BHV Peterburg ISBN 978 5 9775 0360 0 GR 11 l 1182 pages 20 nb 11 German editions edit Ryshik Jossif Moissejewitsch Gradstein Israil Solomonowitsch 1957 Tafeln Tables Summen Produkt und Integral Tafeln Tables of Series Products and Integrals in German and English Translated by Berg Christa Berg Lothar Strauss Martin Foreword by Schroder Kurt Erich de 1 ed Berlin German Democratic Republic Deutscher Verlag der Wissenschaften LCCN 58028629 DNB IDN 454242255 Lizenz Nr 206 435 2 57 Retrieved 2016 02 21 Gray or green linen xxiii 438 pages 15 16 Errata 65 67 68 69 70 71 72 Ryshik Jossif Moissejewitsch Gradstein Israil Solomonowitsch 1963 Tafeln Tables Summen Produkt und Integral Tafeln Tables of Series Products and Integrals in German and English Translated by Berg Christa Berg Lothar Strauss Martin Foreword by Schroder Kurt Erich de 2nd corrected ed Berlin German Democratic Republic VEB Deutscher Verlag der Wissenschaften DVW LCCN 63025905 DNB IDN 579497747 Lizenz Nr 206 435 93 63 Retrieved 2016 02 21 110 Printed by VEB Druckerei Thomas Muntzer Bad Langensalza Distributed in the USA by Plenum Press Inc New York Green linen xxiii 438 pages 4 page errata inlet Errata 70 nbsp Cover of third German English edition 1981Gradstein Israil Solomonowitsch Ryshik Jossif Moissejewitsch 1981 Geronimus Juri Weneaminowitsch Zeitlin Michael Juljewitsch eds Tafeln Tables Summen Produkt und Integraltafeln Tables of Series Products and Integrals in German and English Translated by Boll Ludwig 3 ed Berlin Thun Frankfurt am Main Moscow Verlag Harri Deutsch Verlag MIR Moscow ISBN 3 87144 350 6 LCCN 82202345 DNB IDN 551448512 881086274 881086282 Gray linen with gilded embossing by A W Schipow 2 volumes 677 3 amp 504 pages 73 74 Polish edition edit Ryzyk I M Gradsztejn I S 1964 Tablice calek sum szeregow i iloczynow in Polish Translated by Malesinski Roman 1 ed Warsaw Poland Panstwowe Wydawnictwo Naukowe PWN OCLC 749996828 VIAF 309184374 Retrieved 2016 02 16 Light grayish cover 464 pages English editions edit Gradshteyn Izrail Solomonovich Ryzhik Iosif Moiseevich Geronimus Yuri Veniaminovich Tseytlin Michail Yulyevich February 1966 1965 Jeffrey Alan ed Table of Integrals Series and Products Translated by Scripta Technica Inc 3 ed Academic Press ISBN 0 12 294750 9 LCCN 65029097 Retrieved 2016 02 21 Black cloth hardcover with gilt titles white dust jacket xiv 1086 pages 1 Errata 1 72 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 Gradshteyn Izrail Solomonovich Ryzhik Iosif Moiseevich Geronimus Yuri Veniaminovich Tseytlin Michail Yulyevich 1980 Jeffrey Alan ed Table of Integrals Series and Products Translated by Scripta Technica Inc 4th corrected and enlarged ed Academic Press Inc ISBN 978 0 12 294760 5 GR 4 5 6 7 Retrieved 2016 02 21 xlvi 1160 pages 2 17 Errata 2 17 93 94 95 96 97 98 99 100 101 nbsp Cover of fifth English edition 1994Gradshteyn Izrail Solomonovich Ryzhik Iosif Moiseevich Geronimus Yuri Veniaminovich Tseytlin Michail Yulyevich January 1994 Jeffrey Alan ed Table of Integrals Series and Products Translated by Scripta Technica Inc 5 ed Academic Press Inc MR 1243179 Retrieved 2016 02 21 Blue hardcover with green or blue rectangular and gilt titles xlvii 1204 pages 3 18 4 5 A CD ROM version with ISBN 0 12 294756 8 ISBN 978 0 12 294756 8 and LCCN 96 801532 was prepared by Lightbinders Inc in July 1996 102 103 4 5 Errata 3 104 105 106 107 4 5 108 nbsp Cover of sixth English edition 2000Gradshteyn Izrail Solomonovich Ryzhik Iosif Moiseevich Geronimus Yuri Veniaminovich Tseytlin Michail Yulyevich July 2000 Jeffrey Alan Zwillinger Daniel eds Table of Integrals Series and Products Translated by Scripta Technica Inc 6 ed Academic Press Inc ISBN 978 0 12 294757 5 MR 1773820 GR 10 Retrieved 2016 02 21 Red cover xlvii 1163 pages 109 A reprint edition 积分 级数和乘积表 by World Books Press became available in China under ISBN 7 5062 6546 X ISBN 978 7 5062 6546 1 in April 2004 Errata 32 41 45 109 110 111 112 113 Gradshteyn Izrail Solomonovich Ryzhik Iosif Moiseevich Geronimus Yuri Veniaminovich Tseytlin Michail Yulyevich February 2007 Jeffrey Alan Zwillinger Daniel eds Table of Integrals Series and Products Translated by Scripta Technica Inc 7 ed Academic Press Inc ISBN 978 0 12 373637 6 MR 2360010 GR 11 Retrieved 2016 02 21 111 112 xlviii 1171 pages with CD ROM 19 114 A reprint edition 积分 级数和乘积表 by Beijing World Publishing Corporation 世界图书出版公司北京公司 WPCBJ became available in China under ISBN 7 5062 8235 6 ISBN 978 7 5062 8235 2 in May 2007 Errata 41 45 47 51 53 57 59 115 Gradshteyn Izrail Solomonovich Ryzhik Iosif Moiseevich Geronimus Yuri Veniaminovich Tseytlin Michail Yulyevich Jeffrey Alan 2015 October 2014 Zwillinger Daniel Moll Victor Hugo eds Table of Integrals Series and Products Translated by Scripta Technica 8 ed Academic Press Inc ISBN 978 0 12 384933 5 GR 12 Retrieved 2016 02 21 xlvi 1133 pages 21 Errata 116 30 117 Japanese edition edit Gradshtejn Guradoshu グラドシュ I S Ryzhik Rijiku リジク I M December 1983 Sugaku daikōshikishu 数学大公式集 Large mathematics collection in Japanese Translated by Otsuki Yoshihiko 大槻 義彦 in Japanese 1 ed Tokyo Japan Maruzen de 丸善 ISBN 978 4 621 02796 7 NCID BN00561932 JPNO JP84018271 Retrieved 2016 04 06 xv 1085 pages See also editPrudnikov Brychkov and Marichev PBM Bronshtein and Semendyayev BS Abramowitz and Stegun AS NIST Handbook of Mathematical Functions DLMF Jahnke and Emde JE Magnus and Oberhettinger MO Notes edit 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 a b c Iosif Moiseevich Ryzhik Iosif Moiseevich Ryzhik 6 1918 1941 VIAF 15286520 GND 107340518 1087809320 1 2 NB Some sources identify him as a sergeant serzhantom born in 1918 originally from Vitebsk Vitebska who was drafted into the army in 1939 from Chkalovsk Chkalovska Orenburg Orenburg and got missing in December 1941 3 However since a birth year 1918 would have made him a very young author 18 this could also have been a namesake In the foreword of the first edition of the book Ryzhik thanked three mathematicians of the Moscow Mathematical Society for their suggestions and advice Vyacheslav Vassilievich Stepanov Vyacheslav Vasilevich Stepanov Aleksei Ivanovich Markushevich Aleksej Ivanovich Markushevich and Ilya Nikolaevich Bronshtein Ilya Nikolaevich Bronshtejn suggesting that he must have been in some way associated with this group a b Izrail Solomonovich Gradshteyn Izrail Solomonovich Gradshtejn 1899 Odessa 1958 Moscow VIAF 20405466 VIAF 310677818 VIAF 270418384 ISNI 0000000116049405 GND 11526194X a b c d e Following the sources this article distinguishes between the documented number of formulas and the number of entries The fact that Ryzhik s death was not announced before the third edition of the book in 1951 might indicate that his status was unclear for a number of years or in the case of the first edition that typesetting had already started but actual production of the book had to be delayed and was then finalized in his absence as a consequence of the war Yuri Veniaminovich Geronimus Yurij Veneaminovich Geronimus 1923 2013 GND 131451812 Michail Yulyevich Tseytlin Mihail Yu levich Cejtlin also as M Yu Ceitlin Michael Juljewitsch Zeitlin Michael Juljewitsch Zeitlein Michael Juljewitsch Tseitlin Mikhail Juljewitsch Tseitlin Christa Berg nee Jahncke GND 122341597 this entry contains an incorrect birth year and some incorrectly associated books 4 Lothar Berg 1930 07 28 to 2015 07 27 GND 117708054 5 6 Martin D H Strauss also as Martin D H Strauss 1907 03 18 Pillau Baltijsk Ostpreussen 1978 05 17 East Berlin GDR GND 139569200 German physicist and philosopher 7 8 9 10 11 Ludwig Boll 1911 12 10 Gaulsheim Germany 1984 12 02 GND 1068090308 German mathematician 12 13 a b c d The seventh Russian edition 2011 was named after the seventh English edition 2007 of which it was a retranslation There was no sixth genuinely Russian edition The English series of editions was originally 1965 based on the fourth Russian edition 1962 1963 It is unknown if any changes for the fifth Russian edition 1971 or the third German English edition 1981 which did incorporate material from the fifth Russian edition were reflected in any of the English editions in between and thereby in the seventh Russian edition as well a b Alan Jeffrey 1929 07 16 to 2010 06 06 GND 113118120 14 15 16 Daniel Dan Ian Zwillinger 1957 GND 172475694 17 Victor Hugo Moll 1956 GND 173099572 References edit a b c d Shanks Daniel October 1966 Reviews and Descriptions of Tables and Books 85 Table of Integrals Series and Products by I S Gradshteyn I M Ryzhik PDF Mathematics of Computation review 20 96 616 617 doi 10 2307 2003554 JSTOR 2003554 RMT 85 Retrieved 2016 03 04 a b c d Luke Yudell Leo January 1981 Reviews and Descriptions of Tables and Books 5 I S Gradshteyn and I M Ryzhik Tables of Integrals Series and Products Academic Press New York 1980 PDF Mathematics of Computation review 36 153 310 314 doi 10 2307 2007757 JSTOR 2007757 MSC 7 95 7 100 Retrieved 2016 03 04 a b c d Kolbig Kurt Siegfried January 1995 Reviews and Descriptions of Tables and Books 1 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 5th ed Alan Jeffrey ed Academic Press Boston 1994 PDF Mathematics of Computation 64 209 439 441 doi 10 2307 2153347 JSTOR 2153347 MSC 00A22 33 00 44 00 65 00 Retrieved 2016 03 03 a b c d Wimp Jet April 1997 Tables of Integrals Series and Products By I S Gradshteyn and I M Ryzhik edited by Alan Jeffrey American Mathematical Monthly a b c d Wimp Jet October 1997 1997 09 30 Koepf Wolfram ed 2 Tables of Integrals Series and Products By I S Gradshteyn and I M Ryzhik edited by Alan Jeffrey PDF Books and Journals Reviews Orthogonal Polynomials and Special Functions Vol 8 no 1 SIAM Activity Group on Orthogonal Polynomials and Special Functions pp 13 16 Archived PDF from the original on 2022 01 20 Retrieved 2022 01 23 a b c d e f g h i j k Wolfram Stephen 2005 10 08 The History and Future of Special Functions Wolfram Technology Conference Festschrift for Oleg Marichev in honor of his 60th birthday speech blog post Champaign IL USA Stephen Wolfram LLC The story behind Gradshteyn Ryzhik Archived from the original on 2016 04 07 Retrieved 2016 04 06 In 1936 Iosif Moiseevich Ryzhik had a book entitled Special Functions published by the United Moscow Leningrad Scientific Technical Publisher Ryzhik died in 1941 either during the siege of Leningrad or fighting on the Russian front In 1943 a table of formulas was published under Ryzhik s name by the Governmental Moscow Leningrad Technical Theoretical Publisher The only thing the book seems to say about its origins is that it s responding to the shortage of books of formulas It says that some integrals marked in it are original but the others mostly come from three books a French one from 1858 a German one from 1894 and an American one from 1922 It explains that effort went into the ordering of the integrals and that some are simplified by using a new special function s equal to Gamma x y 1 Gamma x Gamma y It then thanks three fairly prominent mathematicians from Moscow University That s basically all we know about Ryzhik Israil Solomonovitch Gradshteyn was born in 1899 in Odessa and became a professor of mathematics at Moscow State University But in 1948 he was fired as part of the Soviet attack on Jewish academics To make money he wanted to write a book And so he decided to build on Ryzhik s tables Apparently he never met Ryzhik But he created a new edition and by the third edition the book was known as Gradshteyn Ryzhik Gradshteyn died of natural causes in Moscow in 1958 Though somehow there developed an urban legend that one of the authors of Gradshteyn Ryzhik had been shot as a piece of anti Semitism on the grounds that an error in their tables had caused an airplane crash Meanwhile starting around 1953 Yurii Geronimus who had met Gradshteyn at Moscow State University began helping with the editing of the tables and actually added the appendices on special functions Later on several more people were involved And when the tables were published in the West there were arguments about royalties But Geronimus in 2005 was still alive and well and living in Jerusalem and Oleg phoned him Bierens de Haan David 1867 Nouvelles tables d integrales definies New tables of definite integrals in French 1 ed Leiden Netherlands P Engels Retrieved 2016 04 17 NB This book had a precursor in 1858 named Tables d integrales definies 18 published by C G van der Post in Amsterdam with supplement Supplement aux tables d integrales definies 19 in ca 1864 Cited as BI BH in GR Laska Vaclav Jan 1888 1894 Sammlung von Formeln der reinen und angewandten Mathematik Compilation of formulae of pure and applied mathematics in German Vol 1 3 1 ed Braunschweig Germany Friedrich Vieweg und Sohn de OCLC 24624148 Retrieved 2016 04 17 NB The book writes the author s name as Wenzel Laska Cited as LA La in GR Adams Edwin Plimpton Hippisley Richard Lionel 1922 Greenhill Alfred George ed Smithsonian Mathematical Formulae and Tables of Elliptic Functions Smithsonian Miscellaneous Collections Vol 74 1 ed Washington D C USA Smithsonian Institution Retrieved 2016 04 17 NB Cited as AD A in GR a b Archibald Raymond Clare October 1945 Recent Mathematical Tables 219 I M Ryzhik Tablitsy Integralov Summ Riadov i Proizvedeniĭ Leningrad OGIZ 1943 PDF Mathematical Tables and Other Aids to Computation MTAG 1 12 American Mathematical Society 442 443 RMT 219 Retrieved 2016 03 04 a b Hahn Wolfgang 1950 07 05 Rydzik I M Tabellen fur Integrale Summen Reihen und Produkte 2 Aufl Moskau Leningrad Staatsverlag fur techn theor Lit 1948 Zentralblatt fur Mathematik review in German 34 1 3 Berlin Germany 70 Zbl 0034 07001 Retrieved 2016 02 16 Stepanov Vyacheslav Vassilievich 1936 Preface Specialnye funkcii Sobranie formul i vspomogatelnye tablicy Special functions A collection of formulas and an auxiliary table By Ryzhik Iosif Moiseevich in Russian 1 ed Moscow Leningrad Obedinennoe nauchno tehnicheskoe izdatelstvo ONTI Gostransizd vo Glav red obshetehnich lit ry i nomografii Archived from the original on 2016 04 09 Retrieved 2016 04 09 160 pages Rosenfeld Rozenfeld Boris Abramowitsch Boris Abramovich in German 2003 Math ru Ob Isaake Moiseeviche Yaglome About Isaac Moiseevich Yaglom Mat prosveshenie Mat enlightenment in Russian 25 28 Archived from the original on 2022 01 12 Retrieved 2022 01 12 via math ru vo vremya antisemitskoj kampanii izvestnoj kak borba s kosmopolitizmom byl uvolen vmeste s I M Gelfandom i I S Gradshtejnom during the antisemitic campaign known as the fight against cosmopolitanism he was fired along with I M Gelfand and I S Gradstein a b Bruins Evert Marie in German 1964 01 02 Gradsteĭn I S und I M Ryzik Integral Summen Reihen und Produkttafeln Tablicy integralov summ rjadov i proizvedeniĭ 4 Aufl uberarb unter Mitwirkung von Ju V Geronimus und M Ju Ceĭtlin Moskau Staatsverlag fur physikalisch mathematische Literatur 1962 Zentralblatt fur Mathematik list in German 103 1 38 Zbl 0103 03801 Retrieved 2016 02 16 a b Wrench Jr John William October 1960 Reviews and Descriptions of Tables and Books 69 I M Ryshik amp I S Gradstein Summen Produkt und Integral Tafeln Tables of Series Products and Integrals VEB Deutscher Verlag der Wissenschaften Berlin PDF Mathematics of Computation 14 72 381 382 doi 10 2307 2003905 JSTOR 2003905 RMT 69 Archived PDF from the original on 2016 03 16 Retrieved 2016 03 16 a b Prachar Karl 1959 09 15 Ryshik I M und I S Gradstein Summen Produkt und Integraltafeln Tables of series products and integrals Berlin VEB Deutscher Verlag der Wissenschaften 1957 Zentralblatt fur Mathematik review in German 80 2 337 338 Zbl 0080 33703 Archived from the original on 2016 02 17 Retrieved 2016 02 12 a b c Papp Frank J Gradshteyn I S Ryzhik I M Tables of integrals series and products Corr and enl ed by Alan Jeffrey Incorporating the 4th ed by Yu V Geronimus and M Yu Tseytlin M Yu Tsejtlin Transl from the Russian New York London Toronto Volumes 1 2 German and English Transl Zentralblatt fur Mathematik und ihre Grenzgebiete review 521 193 MR 0582453 Zbl 0521 33001 Retrieved 2016 02 16 a b Gradshteyn I S Ryzhik I M Table of integrals series and products Transl from the Russian by Scripta Technica Inc 5th ed Boston MA Academic Press Inc 1994 Zentralblatt MATH 1994 ISBN 9780122947551 Zbl 0918 65002 Retrieved 2016 02 16 a b Gradshteyn Izrail Solomonovich Ryzhik Iosif Moiseevich Geronimus Yuri Veniaminovich Tseytlin Michail Yulyevich February 2007 Jeffrey Alan Zwillinger Daniel eds Table of Integrals Series and Products Translated by Scripta Technica 7 ed Academic Press Inc ISBN 978 0 12 373637 6 MR 2360010 GR 11 Retrieved 2016 02 21 20 a b Tablicy integralov ryada i produktov Table of Integrals Series and Products PDF in Russian 7 ed BHV BHV Peterburg 2011 ISBN 978 5 9775 0360 0 Archived PDF from the original on 2016 03 16 Retrieved 2016 03 16 a b c Gradshteyn Izrail Solomonovich Ryzhik Iosif Moiseevich Geronimus Yuri Veniaminovich Tseytlin Michail Yulyevich Jeffrey Alan 2015 October 2014 Zwillinger Daniel Moll Victor Hugo eds Table of Integrals Series and Products Translated by Scripta Technica 8 ed Academic Press Inc ISBN 978 0 12 384933 5 GR 12 Retrieved 2016 02 21 a b c Jeffrey Alan 1995 01 01 Handbook of Mathematical Formulas and Integrals 1 ed Academic Press Inc ISBN 978 0 12 382580 3 Jeffrey Alan 2000 08 01 Handbook of Mathematical Formulas and Integrals 2 ed Academic Press Inc ISBN 978 0 12 382251 2 Jeffrey Alan 2004 Handbook of Mathematical Formulas and Integrals 3 ed Academic Press Inc published 2003 11 21 ISBN 978 0 12 382256 7 Archived from the original on 2022 01 01 Retrieved 2016 03 01 a b Jeffrey Alan Dai Hui Hui 2008 02 01 Handbook of Mathematical Formulas and Integrals 4 ed Academic Press Inc ISBN 978 0 12 374288 9 Retrieved 2016 03 01 NB Contents of companion CD ROM 21 22 Vardi Ilan April 1988 Integrals An Introduction to Analytic Number Theory PDF American Mathematical Monthly 95 4 308 315 doi 10 2307 2323562 JSTOR 2323562 Archived PDF from the original on 2016 03 15 Retrieved 2016 03 14 23 Moll Victor Hugo April 2010 2009 08 30 Seized Opportunities PDF Notices of the American Mathematical Society 57 4 476 484 Archived PDF from the original on 2016 04 08 Retrieved 2016 04 08 24 Boros George Moll Victor Hugo 2006 September 2004 Irresistible Integrals Symbolics Analysis and Experiments in the Evaluation of Integrals reprinted 1st ed Cambridge University Press CUP p xi ISBN 978 0 521 79186 1 Retrieved 2016 02 22 25 26 NB This edition contains many typographical errors Moll Victor Hugo Vignat Christophe The integrals in Gradshteyn and Ryzhik Part 29 Chebyshev polynomials PDF Scientia Series A Mathematical Sciences Archived from the original on 2016 03 13 Retrieved 2016 03 13 a href Template Cite journal html title Template Cite journal cite journal a CS1 maint unfit URL link NB This paper discusses 19 GR entries 1 14 2 1 1 320 2 18 1 9 3 753 2 3 771 8 6 611 7 341 1 7 341 2 7 342 7 343 1 7 344 1 7 344 2 7 346 7 348 7 349 7 355 1 7 355 2 8 411 1 8 921 27 a b Amdeberhan Tewodros Dixit Atul Guan Xiao Jiu Lin Kuznetsov Alexey Moll Victor Hugo Vignat Christophe The integrals in Gradshteyn and Ryzhik Part 30 Trigonometric functions PDF Scientia Series A Mathematical Sciences Archived from the original on 2016 03 13 Retrieved 2016 03 13 a href Template Cite journal html title Template Cite journal cite journal a CS1 maint unfit URL link NB This paper discusses 51 GR entries 1 320 1 1 320 3 1 320 5 1 320 7 2 01 5 2 01 6 2 01 7 2 01 8 2 01 9 2 01 10 2 01 11 2 01 12 2 01 13 2 01 14 2 513 1 2 513 2 2 513 3 2 513 4 3 231 5 3 274 2 3 541 8 3 611 3 3 621 3 3 621 4 3 624 6 3 631 16 3 661 3 3 661 4 3 675 1 3 675 2 3 688 1 3 721 1 3 747 7 3 761 4 4 381 1 4 381 2 4 381 3 4 381 4 4 521 1 6 671 7 6 671 8 7 244 1 7 244 2 7 531 1 7 531 2 8 230 1 8 230 2 8 361 7 8 370 8 910 2 8 911 1 It also contains 1 errata for GR entry 3 541 8 28 Gonzalez Ivan Kohl Karen T Moll Victor Hugo 2014 06 13 2014 03 19 Evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets PDF Scientia Series A Mathematical Sciences 25 published 2014 65 84 Retrieved 2016 03 13 NB This paper is also incorporated into volume II a b Moll Victor Hugo 2006 11 06 2006 07 21 The integrals in Gradshteyn and Ryzhik Part 1 A family of logarithmic integrals PDF Scientia Series A Mathematical Sciences 14 published 2007 1 6 Archived from the original PDF on 2017 02 02 Retrieved 2016 03 14 29 NB This paper from volume I discusses 10 GR entries 3 419 2 3 419 3 3 419 4 3 419 5 3 419 6 4 232 3 4 261 4 4 262 3 4 263 1 4 264 3 30 Moll Victor Hugo 2006 11 06 2006 06 27 The integrals in Gradshteyn and Ryzhik Part 2 Elementary logarithmic integrals PDF Scientia Series A Mathematical Sciences 14 published 2007 7 15 Retrieved 2016 03 14 31 NB This paper from volume I discusses 5 GR entries 4 231 1 4 231 5 4 231 6 4 232 1 4 232 2 32 Moll Victor Hugo 2007 01 16 2006 12 27 The integrals in Gradshteyn and Ryzhik Part 3 Combinations of logarithms and exponentials PDF Scientia Series A Mathematical Sciences 15 published 2007 31 36 arXiv 0705 0175 Retrieved 2016 03 14 33 NB This paper from volume I discusses 8 GR entries 4 331 1 4 335 1 4 335 3 4 352 1 4 352 2 4 352 3 4 352 4 4 353 2 34 Moll Victor Hugo 2007 01 16 2006 12 27 The integrals in Gradshteyn and Ryzhik Part 4 The gamma function PDF Scientia Series A Mathematical Sciences 15 published 2007 37 46 arXiv 0705 0179 Retrieved 2016 03 14 35 NB This paper from volume I discusses 44 GR entries 3 324 2 3 326 1 3 326 2 3 328 3 351 3 3 371 3 381 4 3 382 2 3 434 1 3 434 2 3 461 2 3 461 3 3 462 9 3 471 3 3 478 1 3 478 2 3 481 1 3 481 2 4 215 1 4 215 2 4 215 3 4 215 4 4 229 1 4 229 3 4 229 4 4 269 3 4 272 5 4 272 6 4 272 7 4 325 8 4 325 11 4 325 12 4 331 1 4 333 4 335 1 4 335 3 4 355 1 4 355 3 4 355 4 4 358 2 4 358 3 4 358 4 4 369 1 4 369 2 36 Amdeberhan Tewodros Medina Luis A Moll Victor Hugo 2007 01 16 2006 12 27 The integrals in Gradshteyn and Ryzhik Part 5 Some trigonometric integrals PDF Scientia Series A Mathematical Sciences 15 published 2007 47 60 arXiv 0705 2379 Retrieved 2016 03 14 37 38 NB This paper from volume I discusses 10 GR entries 3 621 1 3 621 3 3 621 4 3 761 11 3 764 1 3 764 2 3 821 3 3 821 14 3 822 1 3 822 2 39 Moll Victor Hugo 2007 10 31 2007 08 31 The integrals in Gradshteyn and Ryzhik Part 6 The beta function PDF Scientia Series A Mathematical Sciences 16 published 2008 9 24 arXiv 0707 2121 Retrieved 2016 03 14 40 NB This paper from volume I discusses 65 GR entries 3 191 1 3 191 2 3 191 3 3 192 1 3 192 2 3 193 3 194 3 3 194 4 3 194 6 3 194 7 3 196 2 3 196 3 3 196 4 3 196 5 3 216 1 3 216 2 3 217 3 218 3 221 1 3 221 2 3 222 2 3 223 1 3 223 2 3 223 3 3 224 3 225 1 3 225 2 3 225 3 3 226 1 3 226 2 3 241 2 3 241 4 3 241 5 3 248 1 3 248 2 3 248 3 3 249 1 3 249 2 3 249 5 3 249 7 3 249 8 3 251 1 3 251 2 3 251 3 3 251 4 3 251 5 3 251 6 3 251 8 3 251 9 3 251 10 3 251 11 3 267 1 3 267 2 3 267 3 3 311 3 3 311 9 3 312 1 3 313 1 3 313 2 3 314 3 457 3 4 251 1 4 273 4 275 1 4 321 1 41 Amdeberhan Tewodros Moll Victor Hugo 2007 10 31 2007 08 21 The integrals in Gradshteyn and Ryzhik Part 7 Elementary examples PDF Scientia Series A Mathematical Sciences 16 published 2008 25 39 arXiv 0707 2122 Retrieved 2016 03 14 42 NB This paper from volume I discusses 30 GR entries 2 321 1 2 321 2 2 322 1 2 322 2 2 322 3 2 322 4 3 195 3 248 4 3 248 6 3 249 1 3 249 6 3 252 1 3 252 2 3 252 3 3 268 1 3 310 3 311 1 3 351 1 3 351 2 3 351 7 3 351 8 3 351 9 3 353 4 3 411 19 3 411 20 3 471 1 3 622 3 3 622 4 4 212 7 4 222 1 43 Moll Victor Hugo Rosenberg Jason Straub Armin Whitworth Pat 2007 10 31 2007 08 31 The integrals in Gradshteyn and Ryzhik Part 8 Combinations of powers exponentials and logarithms PDF Scientia Series A Mathematical Sciences 16 published 2008 41 50 arXiv 0707 2123 Retrieved 2016 03 14 44 NB This paper from volume I discusses 7 GR entries 3 351 1 4 331 1 4 351 1 4 351 2 4 353 3 4 362 1 8 350 1 45 Amdeberhan Tewodros Moll Victor Hugo Rosenberg Jason Straub Armin Whitworth Pat 2008 11 18 2007 11 29 The integrals in Gradshteyn and Ryzhik Part 9 Combinations of logarithms rational and trigonometric functions PDF Scientia Series A Mathematical Sciences 17 published 2009 27 44 Retrieved 2016 03 14 46 NB This paper from volume I discusses 45 GR entries 2 148 4 3 747 7 4 223 1 4 223 2 4 224 1 4 224 2 4 224 3 4 224 4 4 224 5 4 224 6 4 225 1 4 225 2 4 227 1 4 227 2 4 227 3 4 227 9 4 227 10 4 227 11 4 227 13 4 227 14 4 227 15 4 231 1 4 231 2 4 231 3 4 231 4 4 231 8 4 231 9 4 231 11 4 231 12 4 231 13 4 231 14 4 231 15 4 231 19 4 231 20 4 233 1 4 261 8 4 291 1 4 291 2 4 295 5 4 295 6 4 295 11 4 521 1 4 531 1 8 366 3 8 380 3 47 a b c Medina Luis A Moll Victor Hugo 2008 11 18 2007 11 29 The integrals in Gradshteyn and Ryzhik Part 10 The digamma function PDF Scientia Series A Mathematical Sciences 17 published 2009 45 66 Retrieved 2016 03 14 48 49 NB This paper from volume I discusses 76 GR entries 3 219 3 231 1 3 231 3 3 231 5 3 231 6 3 233 3 234 1 3 235 3 244 2 3 244 3 3 265 3 268 2 3 269 1 3 269 3 3 311 5 3 311 6 3 311 7 3 311 8 3 311 10 3 311 11 3 311 12 3 312 2 3 316 3 317 1 3 317 2 3 427 1 3 427 2 3 429 3 434 2 3 435 3 3 435 4 3 442 3 3 457 1 3 463 3 467 3 469 2 3 469 3 3 471 14 3 475 1 3 475 2 3 475 3 3 476 1 3 476 2 4 241 1 4 241 2 4 241 3 4 241 4 4 241 5 4 241 7 4 241 8 4 241 9 4 241 10 4 241 11 4 243 4 244 1 4 244 2 4 244 3 4 245 1 4 245 2 4 246 4 247 1 4 247 2 4 251 4 4 253 1 4 254 1 4 254 6 4 256 4 271 15 4 275 2 4 281 1 4 281 4 4 281 5 4 293 8 4 293 13 4 331 1 8 371 2 50 Boyadzhiev Khristo N Medina Luis A Moll Victor Hugo 2009 03 16 2008 07 02 The integrals in Gradshteyn and Ryzhik Part 11 The incomplete beta function PDF Scientia Series A Mathematical Sciences 18 published 2009 61 75 Retrieved 2016 03 14 51 52 NB This paper from volume I discusses 52 GR entries 3 222 1 3 231 2 3 231 4 3 241 1 3 244 1 3 249 4 3 251 7 3 269 2 3 311 2 3 311 13 3 522 4 3 541 6 3 541 7 3 541 8 3 622 2 3 623 2 3 623 3 3 624 1 3 635 1 3 651 1 3 651 2 3 656 1 3 981 3 4 231 1 4 231 6 4 231 11 4 231 12 4 231 14 4 231 19 4 231 20 4 234 1 4 234 2 4 251 3 4 254 4 4 261 2 4 261 6 4 261 11 4 262 1 4 262 4 4 263 2 4 264 1 4 265 4 266 1 4 271 1 4 271 16 8 361 7 8 365 4 8 366 3 8 366 11 8 366 12 8 366 13 8 370 53 Moll Victor Hugo Posey Ronald A 2009 03 16 2008 07 02 The integrals in Gradshteyn and Ryzhik Part 12 Some logarithmic integrals PDF Scientia Series A Mathematical Sciences 18 published 2009 77 84 Retrieved 2016 03 14 54 NB This paper from volume I discusses 6 GR entries 4 231 1 4 233 1 4 233 2 4 233 3 4 233 4 4 261 8 55 Moll Victor Hugo 2010 10 10 2009 07 07 The integrals in Gradshteyn and Ryzhik Part 13 Trigonometric forms of the beta function PDF Scientia Series A Mathematical Sciences 19 published 2010 91 96 arXiv 1004 2439 Retrieved 2016 03 14 56 NB This paper from volume I discusses 21 GR entries 3 621 1 3 621 2 3 621 3 3 621 4 3 621 5 3 621 6 3 621 7 3 622 1 3 623 1 3 624 2 3 624 3 3 624 4 3 624 5 3 625 1 3 625 2 3 625 3 3 625 4 3 626 1 3 626 2 3 627 3 628 57 a b c Amdeberhan Tewodros Moll Victor Hugo 2010 10 10 2009 07 07 The integrals in Gradshteyn and Ryzhik Part 14 An elementary evaluation of entry 3 411 5 PDF Scientia Series A Mathematical Sciences 19 published 2010 97 103 arXiv 1004 2440 Retrieved 2016 03 14 58 NB This paper from volume I discusses 1 GR entry 3 411 5 59 Albano Matthew Amdeberhan Tewodros Beyerstedt Erin Moll Victor Hugo 2010 07 18 2010 04 20 The integrals in Gradshteyn and Ryzhik Part 15 Frullani integrals PDF Scientia Series A Mathematical Sciences 19 published 2010 113 119 arXiv 1005 2940 Retrieved 2016 03 14 60 NB This paper from volume I discusses 12 GR entries 3 232 3 329 3 412 1 3 434 2 3 436 3 476 1 3 484 4 267 8 4 297 7 4 319 3 4 324 2 4 536 2 61 a b Boettner Stefan Thomas Moll Victor Hugo 2010 07 21 2010 03 22 The integrals in Gradshteyn and Ryzhik Part 16 Complete elliptic integrals PDF Scientia Series A Mathematical Sciences 20 published 2010 45 59 arXiv 1005 2941 Retrieved 2016 03 14 62 NB This paper from volume II discusses 36 GR entries 1 421 1 3 166 16 3 166 18 3 721 1 3 821 7 3 841 1 3 841 2 3 841 3 3 841 4 3 842 3 3 842 4 3 844 1 3 844 2 3 844 3 3 844 4 3 844 5 3 844 6 3 844 7 3 844 8 3 846 1 3 846 2 3 846 3 3 846 4 3 846 5 3 846 6 3 846 7 3 846 8 4 242 1 4 395 1 4 414 1 4 432 1 4 522 4 4 522 5 4 522 6 4 522 7 8 129 1 63 Amdeberhan Tewodros Boyadzhiev Khristo N Moll Victor Hugo 2010 07 21 2010 03 22 The integrals in Gradshteyn and Ryzhik Part 17 The Riemann zeta function PDF Scientia Series A Mathematical Sciences 20 published 2010 61 71 Retrieved 2016 03 14 64 NB This paper from volume II discusses 36 GR entries 3 333 1 3 333 2 3 411 1 3 411 2 3 411 3 3 411 4 3 411 6 3 411 7 3 411 8 3 411 9 3 411 10 3 411 11 3 411 12 3 411 13 3 411 14 3 411 15 3 411 17 3 411 18 3 411 21 3 411 22 3 411 25 3 411 26 4 231 1 4 231 2 4 261 12 4 261 13 4 262 1 4 262 2 4 262 5 4 262 6 4 264 1 4 264 2 4 266 1 4 266 2 4 271 1 4 271 2 65 Koutschan Christoph Moll Victor Hugo 2010 08 21 2010 04 26 The integrals in Gradshteyn and Ryzhik Part 18 Some automatic proofs PDF Scientia Series A Mathematical Sciences 20 published 2010 93 111 Archived PDF from the original on 2016 03 14 Retrieved 2016 03 14 66 67 NB This paper from volume II discusses 7 GR entries 2 148 3 3 953 4 535 1 6 512 1 7 322 7 349 7 512 5 68 Albano Matthew Amdeberhan Tewodros Beyerstedt Erin Moll Victor Hugo 2011 04 13 2010 12 23 The integrals in Gradshteyn and Ryzhik Part 19 The error function PDF Scientia Series A Mathematical Sciences 21 published 2011 25 42 Retrieved 2016 03 14 69 NB This paper from volume II discusses 42 GR entries 3 321 1 3 321 2 3 321 3 3 321 4 3 321 5 3 321 6 3 321 7 3 322 1 3 322 2 3 323 1 3 323 2 3 325 3 361 1 3 361 2 3 361 3 3 362 1 3 362 2 3 363 1 3 363 2 3 369 3 382 4 3 461 5 3 462 5 3 462 6 3 462 7 3 462 8 3 464 3 466 1 3 466 2 3 471 15 3 471 16 3 472 1 6 281 1 6 282 1 6 283 1 6 283 2 6 294 1 8 258 1 8 258 2 8 258 3 8 258 4 8 258 5 70 a b Kohl Karen T Moll Victor Hugo 2011 04 13 2010 12 23 The integrals in Gradshteyn and Ryzhik Part 20 Hypergeometric functions PDF Scientia Series A Mathematical Sciences 21 published 2011 43 54 Retrieved 2016 03 14 71 NB This paper from volume II discusses 26 GR entries 3 194 1 3 194 2 3 194 5 3 196 1 3 197 1 3 197 2 3 197 3 3 197 4 3 197 5 3 197 6 3 197 7 3 197 8 3 197 9 3 197 10 3 197 11 3 197 12 3 198 3 199 3 227 1 3 254 1 3 254 2 3 259 2 3 312 3 3 389 1 9 121 4 9 131 1 72 Boyadzhiev Khristo N Moll Victor Hugo 2012 10 20 2012 05 15 The integrals in Gradshteyn and Ryzhik Part 21 Hyperbolic functions PDF Scientia Series A Mathematical Sciences 22 published 2012 109 127 Archived PDF from the original on 2016 03 14 Retrieved 2016 03 14 NB This paper from volume II discusses 75 GR entries 2 423 9 3 231 2 3 231 5 3 265 3 511 1 3 511 2 3 511 4 3 511 5 3 511 8 3 512 1 3 512 2 3 521 1 3 521 2 3 522 3 3 522 6 3 522 8 3 522 10 3 523 2 3 523 3 3 523 4 3 523 5 3 523 6 3 523 7 3 523 8 3 523 9 3 523 10 3 523 11 3 523 12 3 524 2 3 524 4 3 524 6 3 524 8 3 524 9 3 524 10 3 524 11 3 524 12 3 524 13 3 524 14 3 524 15 3 524 16 3 524 17 3 524 18 3 524 19 3 524 20 3 524 21 3 524 22 3 524 23 3 525 1 3 525 2 3 525 3 3 525 4 3 525 5 3 525 6 3 525 7 3 525 8 3 527 1 3 527 2 3 527 3 3 527 4 3 527 5 3 527 6 3 527 7 3 527 8 3 527 9 3 527 10 3 527 11 3 527 12 3 527 13 3 527 14 3 527 15 3 527 16 3 543 2 4 113 3 4 231 12 8 365 9 73 a b Glasser Larry Kohl Karen T Koutschan Christoph Moll Victor Hugo Straub Armin 2012 10 20 2012 05 15 The integrals in Gradshteyn and Ryzhik Part 22 Bessel K functions PDF Scientia Series A Mathematical Sciences 22 published 2012 129 151 Archived PDF from the original on 2016 03 14 Retrieved 2016 03 14 74 NB This paper from volume II discusses 36 GR entries 3 323 3 3 324 1 3 337 1 3 364 3 3 365 2 3 366 2 3 372 3 383 3 3 383 8 3 387 1 3 387 3 3 387 6 3 388 2 3 389 4 3 391 3 395 1 3 461 6 3 461 7 3 461 8 3 461 9 3 462 20 3 462 21 3 462 22 3 462 23 3 462 24 3 462 25 3 469 1 3 471 4 3 471 8 3 471 9 3 471 12 3 478 4 3 479 1 3 547 2 3 547 4 8 432 6 75 Medina Luis A Moll Victor Hugo 2012 06 25 2012 02 01 The integrals in Gradshteyn and Ryzhik Part 23 Combination of logarithms and rational functions PDF Scientia Series A Mathematical Sciences 23 published 2012 1 18 Retrieved 2016 03 14 76 77 NB This paper from volume II discusses 54 GR entries 3 417 1 3 417 2 4 212 7 4 224 5 4 224 6 4 225 1 4 225 2 4 231 1 4 231 2 4 231 8 4 231 9 4 231 10 4 231 11 4 231 16 4 231 17 4 231 18 4 233 1 4 234 3 4 234 6 4 234 7 4 234 8 4 262 7 4 262 8 4 262 9 4 291 1 4 291 2 4 291 3 4 291 4 4 291 5 4 291 6 4 291 7 4 291 8 4 291 9 4 291 10 4 291 11 4 291 12 4 291 13 4 291 14 4 291 15 4 291 16 4 291 17 4 291 18 4 291 19 4 291 20 4 291 21 4 291 22 4 291 23 4 291 24 4 291 25 4 291 26 4 291 27 4 291 28 4 291 29 4 291 30 78 McInturff Kim Moll Victor Hugo 2012 07 28 2012 02 01 The integrals in Gradshteyn and Ryzhik Part 24 Polylogarithm functions PDF Scientia Series A Mathematical Sciences 23 published 2012 45 51 Retrieved 2016 03 14 79 NB This paper from volume II discusses 10 GR entries 3 418 1 3 514 1 3 531 1 3 531 2 3 531 3 3 531 4 3 531 5 3 531 6 3 531 7 9 513 1 80 Moll Victor Hugo 2012 07 28 2012 02 01 The integrals in Gradshteyn and Ryzhik Part 25 Evaluation by series PDF Scientia Series A Mathematical Sciences 23 published 2012 53 65 Retrieved 2016 03 14 81 NB This paper from volume II discusses 18 GR entries 3 194 8 3 311 4 3 342 3 451 1 3 451 2 3 466 3 3 747 7 4 221 1 4 221 2 4 221 3 4 251 5 4 251 6 4 269 1 4 269 2 8 339 1 8 339 2 8 365 4 8 366 3 82 a b Boyadzhiev Khristo N Moll Victor Hugo 2015 01 30 2014 09 19 The integrals in Gradshteyn and Ryzhik Part 26 The exponential integral PDF Scientia Series A Mathematical Sciences 26 published 2015 19 30 Retrieved 2016 03 14 83 NB This paper from volume II discusses 41 GR entries 3 327 3 351 4 3 351 5 3 351 6 3 352 1 3 352 2 3 352 3 3 352 4 3 352 5 3 352 6 3 353 1 3 353 2 3 353 3 3 353 4 3 353 5 3 354 1 3 354 2 3 354 3 3 354 4 3 355 1 3 355 2 3 355 3 3 355 4 3 356 1 3 356 2 3 356 3 3 356 4 3 357 1 3 357 2 3 357 3 3 357 4 3 357 5 3 357 6 3 358 1 3 358 2 3 358 3 3 358 4 4 211 1 4 211 2 4 212 1 4 212 2 84 Medina Luis A Moll Victor Hugo 2015 01 30 2014 09 16 The integrals in Gradshteyn and Ryzhik Part 27 More logarithmic examples PDF Scientia Series A Mathematical Sciences 26 published 2015 31 47 Retrieved 2016 03 14 85 NB This paper from volume II discusses 37 GR entries 3 194 3 3 231 1 3 231 5 3 231 6 3 241 3 3 621 3 3 621 5 4 224 2 4 231 1 4 231 2 4 231 8 4 233 5 4 234 4 4 234 5 4 235 1 4 235 2 4 235 3 4 235 4 4 241 5 4 241 6 4 241 7 4 241 11 4 251 1 4 251 2 4 252 1 4 252 2 4 252 3 4 252 4 4 254 2 4 254 3 4 255 2 4 255 3 4 257 1 4 261 9 4 261 15 4 261 16 4 297 8 86 a b Dixit Atul Moll Victor Hugo 2015 02 01 2014 09 30 The integrals in Gradshteyn and Ryzhik Part 28 The confluent hypergeometric function and Whittaker functions PDF Scientia Series A Mathematical Sciences 26 published 2015 49 61 Retrieved 2016 03 14 87 NB This paper from volume II discusses 17 GR entries 7 612 1 7 612 2 7 621 1 7 621 2 7 621 3 7 621 4 7 621 5 7 621 6 7 621 7 7 621 8 7 621 9 7 621 10 7 621 11 7 621 12 8 334 2 8 703 9 211 4 88 Moll Victor Hugo 2012 Index of the papers in Revista Scientia with formulas from GR Retrieved 2016 02 17 Moll Victor Hugo 2014 10 01 Special Integrals of Gradshteyn and Ryzhik the Proofs Monographs and Research Notes in Mathematics Vol I 1 ed Chapman and Hall CRC Press Taylor amp Francis Group LLC published 2014 11 12 ISBN 978 1 4822 5651 2 Retrieved 2016 02 12 NB This volume compiles Scientia papers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 from issues 14 to 19 Moll Victor Hugo 2015 08 24 Special Integrals of Gradshteyn and Ryzhik the Proofs Monographs and Research Notes in Mathematics Vol II 1 ed Chapman and Hall CRC Press Taylor amp Francis Group LLC published 2015 10 27 ISBN 978 1 4822 5653 6 Retrieved 2016 02 12 NB This volume compiles 14 Scientia articles from issues 20 21 22 23 25 and 26 including papers 16 17 18 19 20 21 22 23 24 25 26 27 28 and one unnumbered paper a b Ryzik I M Tafeln von Integralen Summen Reihen und Produkten Moskau Leningrad Staatsverlag fur technisch theoretische Literatur 1943 Zentralblatt fur Mathematik list in German 60 1 123 1957 04 01 Zbl 0060 12305 Retrieved 2016 02 16 Prachar Karl 1952 09 01 Ryzik I M und I S Gradstejn Tafeln von Integralen Summen Reihen und Produkten 3 umgearb Aufl Moskau Leningrad Staatsverlag fur technisch theoretische Literatur 1951 Zentralblatt fur Mathematik review in German 44 1 5 133 Zbl 0044 13303 Retrieved 2016 02 16 a b Wrench Jr John William October 1960 Table Errata 293 I M Ryshik amp I S Gradstein Summen Produkt und Integral Tafeln Tables of Series Products and Integrals Deutscher Verlag der Wissenschaften Berlin 1957 PDF Mathematics of Computation 14 72 401 403 JSTOR 2003934 MTE 293 Archived PDF from the original on 2016 03 16 Retrieved 2016 03 16 Gradshtejn I S Ryzhik I M 1971 Errata in 4th edition In Geronimus Yu V Cejtlin M Yu eds Tablicy integralov summ ryadov i proizvedenij in Russian 5 ed Nauka Nauka pp 1101 1108 NB The 8 page errata list in later print runs of the fourth Russian edition affected 189 table entries Ryshik Gradstein Summen Produkt und Integral Tafeln Berichtigungen zur 1 Auflage in German Berlin Germany VEB Deutscher Verlag der Wissenschaften 1962 MR 0175273 NB This brochure was available free of charge from the publisher on request Ryshik Gradstein Tafeln Summen Produkte Integrale Berichtigungen zur 1 Auflage L Enseignement Mathematique Bulletin Bibliographique Livres Nouveaux in French and German 9 5 1963 Retrieved 2016 03 04 Die Berichtigung wird den Interessenten auf Anfrage kostenlos durch den Verlag geliefert Rodman Richard B January 1963 Table Errata 326 I M Ryshik amp I S Gradstein Summen Produkt und Integral Tafeln Deutscher Verlag der Wissenschaften Berlin 1957 PDF Mathematics of Computation 17 81 100 103 JSTOR 2003754 MTE 326 Archived PDF from the original on 2016 03 16 Retrieved 2016 03 16 89 a b Schmieg Glenn M July 1966 Errata 392 I M Ryshik amp I S Gradstein Summen Produkt und Integral Tafeln Tables of Series Products and Integrals VEB Deutscher Verlag der Wissenschaften Berlin 1957 PDF Mathematics of Computation 20 95 468 471 doi 10 2307 2003630 JSTOR 2003630 MTE 392 Archived PDF from the original on 2016 03 16 Retrieved 2016 03 16 Filliben James J at Wikidata January 1970 Table Errata 456 I M Ryshik amp I S Gradstein Summen Produkt und Integral Tafeln VEB Deutscher Verlag der Wissenschaften Berlin 1957 PDF Mathematics of Computation 24 109 239 242 JSTOR 2004912 MTE 456 Archived PDF from the original on 2016 03 16 Retrieved 2016 03 16 a b MacKinnon Robert F January 1972 Table Errata 486 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 26 117 305 307 doi 10 1090 s0025 5718 1972 0415970 6 JSTOR 2004754 MR 0415970 MTE 486 Retrieved 2016 03 04 90 Gradshtejn I S Ryzhik I M Summen Produkt und Integraltafeln Band 1 2 Deutsch und englisch Ubers aus dem Russischen auf der Basis der 5 russ Aufl uberarb von J Geronimus und M Zeitlin Tables of series products and integrals Volumes 1 2 German and English Transl Zentralblatt fur Mathematik und ihre Grenzgebiete list in German 448 395 Zbl 0448 65002 Retrieved 2016 02 16 Gradshtejn I S Ryzhik I M Summen Produkt und Integraltafeln Band 1 2 Deutsch und englisch Ubers aus dem Russischen auf der Basis der 5 russ Aufl uberarb von J Geronimus und M Zeitlin Tables of series products and integrals Volumes 1 2 German and English Transl Zentralblatt fur Mathematik und ihre Grenzgebiete list in German 456 355 Zbl 0456 65001 Retrieved 2016 02 16 Fettis Henry E April 1967 Table Errata 408 I S Gradshteyn amp I M Ryzhik Tables of Integrals Series and Products Fourth Edition Academic Press New York 1965 PDF Mathematics of Computation 21 98 293 295 JSTOR 2004214 MTE 408 Retrieved 2016 03 04 Blake J R Wood Van E Glasser M Lawrence Fettis Henry E Hansen Eldon Robert Patrick Merrell R October 1968 Table Errata 428 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products fourth edition prepared by Yu V Geronimus amp M Yu Tseytlin Academic Press New York 1965 PDF Mathematics of Computation 22 104 903 907 JSTOR 2004606 MR 0239122 MTE 428 Retrieved 2016 03 04 NB See 1972 corrigenda by Fettis and 1979 corrigenda by Anderson Corrington Murlan S Fettis Henry E April 1969 Table Errata 437 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 23 106 467 472 JSTOR 2004471 MR 0415966 Retrieved 2016 03 04 91 92 Bradley Lee C October 1969 Table Errata 446 I S Gradshteyn amp I M Ryzhik Tables of Integrals Series and Products 4th edition Academic Press New York 1965 PDF Mathematics of Computation 23 108 891 892 s15 s17 doi 10 1090 s0025 5718 1969 0415968 8 JSTOR 2004993 MR 0415968 MTE 446 Retrieved 2016 03 04 93 Young A T January 1970 Table Errata 451 A Erdelyi W Magnus F Oberhettinger amp F G Tricomi Tables of Integral Transforms McGraw Hill Book Co New York 1954 PDF Mathematics of Computation 24 109 239 242 doi 10 2307 2004614 JSTOR 2004912 MR 0257656 MTE 451 Archived PDF from the original on 2016 03 16 Retrieved 2016 03 16 94 NB The error also affects entry 3 252 10 on page 297 in GR Muhlhausen Carl W Konowalow Daniel D January 1971 Table Errata 473 I S Gradshteyn amp I M Ryzhik Tables of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 25 113 199 201 JSTOR 2005156 MR 0415969 MTE 473 Retrieved 2016 03 04 95 Nash John C April 1972 Table Errata 492 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 26 118 597 599 JSTOR 2005198 MR 0415971 MTE 492 Retrieved 2016 03 04 96 Fettis Henry E April 1972 Corrigendum MTE 428 Math Comp v 22 1968 pp 903 907 PDF Mathematics of Computation 26 118 601 doi 10 2307 2005199 JSTOR 2005199 MR 0415973 Retrieved 2016 03 04 97 NB This corrigenda applies to MTE 428 Ojo Akin Sadiku J April 1973 Table Errata 503 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 27 122 451 452 doi 10 1090 s0025 5718 1973 0415972 0 JSTOR 2005649 MR 0415972 MTE 503 Retrieved 2016 03 04 98 NB See 1982 corrigenda by Fettis Fettis Henry E April 1982 Corrigenda Ojo Akin Sadiku J 1973 Table Errata 503 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 38 158 657 doi 10 1090 S0025 5718 1982 0645681 X JSTOR 2007312 MR 0645681 Retrieved 2016 03 14 NB This corrigenda applies to MTE 503 Scherzinger Ann October 1976 Table Errata 528 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 30 136 899 doi 10 1090 s0025 5718 1976 0408192 x JSTOR 2005420 MR 0408192 MTE 528 Retrieved 2016 03 04 99 Carr Alistair R April 1977 Table Errata 534 I S Gradshteyn amp I M Ryzhik Tables of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 31 138 614 616 doi 10 1090 s0025 5718 1977 0428676 9 JSTOR 2006446 MR 0428676 MTE 534 Retrieved 2016 03 04 100 Robinson Neville I January 1978 Table Errata 550 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 32 141 317 320 JSTOR 2006287 MR 0478539 MTE 550 Retrieved 2016 03 04 101 Fettis Henry E January 1979 Table Errata 557 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 33 145 430 431 JSTOR 2006060 MTE 557 Retrieved 2016 03 04 Anderson Michael January 1979 Corrigenda p 906 of MTE 428 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 33 145 432 433 doi 10 2307 2006061 JSTOR 2006061 Retrieved 2016 03 04 NB This corrigenda applies to MTE 428 McGregor John Ross April 1979 Table Errata 564 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 33 146 845 846 JSTOR 2006322 MTE 564 Retrieved 2016 03 04 Birtwistle David T October 1979 Table Errata 565 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 33 148 1377 JSTOR 2006476 MTE 565 Retrieved 2016 03 04 Gallas Jason A Carlson October 1980 Table Errata 572 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 35 152 1444 doi 10 1090 S0025 5718 1980 0583522 8 JSTOR 2006418 MR 0583522 MTE 572 Retrieved 2016 03 04 102 103 Fettis Henry E January 1981 Table Errata 577 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 36 153 317 318 doi 10 1090 S0025 5718 1981 0595074 8 JSTOR 2007758 MR 0595074 MTE 577 Retrieved 2016 03 04 Fettis Henry E January 1981 Table Errata 582 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 36 153 315 320 JSTOR 2007758 MR 0595074 MTE 582 Archived PDF from the original on 2016 03 16 Retrieved 2016 03 04 NB See 1982 corrigenda by Fettis Fettis Henry E January 1982 Corrigenda Fettis Henry E 1981 Table Errata 582 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 4th ed Academic Press New York 1965 PDF Mathematics of Computation 38 157 337 doi 10 1090 S0025 5718 1982 0637313 1 JSTOR 2007492 MR 0637313 Archived PDF from the original on 2016 03 16 Retrieved 2016 03 16 NB This corrigenda applies to MTE 582 van Haeringen Hendrik Kok Lambrecht P at Wikidata October 1982 Table Errata 589 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products Corrected and enlarged edition Academic Press New York First printing 1980 PDF Mathematics of Computation 39 160 747 757 doi 10 1090 S0025 5718 1982 0669666 2 JSTOR 2007357 MR 0669666 MTE 589 Retrieved 2016 02 22 104 105 van Haeringen Hendrik Kok Lambrecht P at Wikidata I S Gradshteyn amp I M Ryzhik Tables of integrals series and products Math comput 39 747 757 1982 Zentralblatt fur Mathematik und ihre Grenzgebiete review 521 193 Zbl 0521 33002 Retrieved 2016 02 16 Fettis Henry E Deutsch Emeric Krupnikov Ernst D October 1983 Table Errata 601 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products Corrected and enlarged edition Academic Press New York First Printing 1980 PDF Mathematics of Computation 41 164 780 783 doi 10 1090 S0025 5718 1983 0717727 2 JSTOR 2007718 MR 0717727 MTE 601 Retrieved 2016 03 04 106 Solt Gyorgy October 1986 Table Errata 607 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products corrected and enlarged edition prepared by A Jeffrey Academic Press New York 1980 PDF Mathematics of Computation 47 176 767 768 doi 10 1090 S0025 5718 1986 0856719 2 JSTOR 2008202 MR 0856719 MTE 607 Retrieved 2016 03 03 Errors in the Integral Tables of Gradshteyn and Ryzhik with Correct Results from Mathematica Mathematica Information Centre Wolfram Library Archive Technical Notes Champaign IL USA Wolfram Research Inc 2004 2003 Archived from the original on 2003 04 25 Retrieved 2016 02 16 Errors in the Integral Tables of Gradshteyn and Ryzhik with Correct Results from Mathematica Technical note Champaign IL USA Wolfram Research Inc 2004 2003 Archived from the original on 2004 06 19 Retrieved 2016 03 04 Table of integrals series and products Ed by Alan Jeffrey CD ROM version 1 0 for PC MAC and UNIX computers 5th ed English San Diego CA Academic Press 1996 Zentralblatt MATH 1996 ISBN 9780122947568 Zbl 0918 65001 Retrieved 2016 02 16 Rosenblum Marvin October 1996 Koepf Wolfram ed 4 Table of Integrals Series and Products CD ROM Version 1 0 Edited by Alan Jeffrey PDF Books and Journals Review Orthogonal Polynomials and Special Functions Vol 7 no 1 SIAM Activity Group on Orthogonal Polynomials and Special Functions pp 11 12 Archived PDF from the original on 2022 01 20 Retrieved 2022 01 23 Kolbig Kurt Siegfried June 1996 1995 Corrigenda I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products Fifth edition Academic Press Boston PDF CERN Computing and Networks Division CN 95 15 Retrieved 2016 02 12 Kolbig Kurt Siegfried January 1995 Table errata 617 I S Gradshteyn amp I M Ryzhik Table of Integrals Series and Products 5th ed Alan Jeffrey ed Academic Press Boston 1994 PDF Mathematics of Computation 64 209 449 460 doi 10 1090 S0025 5718 1995 1270626 0 JSTOR 2153354 MR 1270626 MTE 617 Retrieved 2016 03 03 107 Lambert Adeline January 1997 Table Errata 628 Mathematics of Computation 66 217 463 JSTOR 2153671 MR 1388890 MTE 628 Fikioris George October 1998 Table Errata 634 Mathematics of Computation 67 224 1753 1754 JSTOR 2584882 MR 1625064 MTE 634 MSC 00A22 33 00 65 00 Ruderman Dan L 2001 01 22 Errors in Gradshteyn and Ryzhik 5th ed Archived from the original on 2007 02 18 3 381 3 3 411 6 3 721 3 3 761 2 3 761 9 3 897 1 6 561 13 8 350 2 a b Rangarajan Sarukkai Krishnamachari Gradshteyn I S Ryzhik I M Table of integrals series and products Translated from the Russian Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger 6th ed San Diego CA Academic Press Zentralblatt MATH ISBN 9780122947575 Zbl 0981 65001 Retrieved 2016 02 16 Table Errata 636 Mathematics of Computation 71 239 1335 1336 July 2002 JSTOR 2698918 MTE 636 Table Errata 637 Mathematics of Computation 71 239 1335 1336 July 2002 JSTOR 2698918 MTE 637 Zwillinger Daniel Jeffrey Alan 2005 11 10 Errata for Tables of Integrals Series and Products 6th edition by I S Gradshteyn and M Ryzhik edited by Alan Jeffrey and Daniel Zwillinger Academic Press Orlando Florida 2000 ISBN 0 12 294757 6 PDF Archived PDF from the original on 2016 03 08 Retrieved 2016 03 08 NB This list of 64 pages has 398 entries According to Daniel Zwillinger it is incomplete De Vos Alexis 2020 11 09 2009 03 19 Alexis De Vos Universiteit Gent Belgium Archived from the original on 2021 06 13 Retrieved 2022 01 12 Finally he is the proud discoverer of an error in equation 3 454 1 of the Gradshteyn and Ryzhik Tables of integrals series and products See errata for 6th edition by Alan Jeffrey and Daniel Zwillinger pages 1 and 19 The error is now corrected in the 7th edition page 363 with acknowledgement in page xxvi Gradshteyn I S Ryzhik I M Table of integrals series and products Translated from the Russian Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger With one CD ROM Windows Macintosh and UNIX 7th ed Amsterdam Elsevier Academic Press ISBN 978 0 12 373637 6 Zentralblatt MATH ISBN 9780123736376 Zbl 1208 65001 Retrieved 2016 02 16 Zwillinger Daniel Jeffrey Alan 2008 04 11 Errata for Tables of Integrals Series and Products 7th edition by I S Gradshteyn and M Ryzhik edited by Alan Jeffrey and Daniel Zwillinger Academic Press Orlando Florida 2007 ISBN 0 12 373637 4 PDF Archived PDF from the original on 2016 03 08 Retrieved 2016 03 08 NB This list of 7 pages has 42 entries According to Daniel Zwillinger it is incomplete Veestraeten Dirk 2015 07 24 2015 06 21 Written at Amsterdam Netherlands Some remarks generalizations and misprints in the integrals in Gradshteyn and Ryzhik Scientia Series A Mathematical Sciences 26 Valparaiso Chile Universidad Tecnica Federico Santa Maria 115 131 ISSN 0716 8446 S2CID 124124467 Archived PDF from the original on 2021 12 26 Retrieved 2021 12 26 18 pages Zwillinger Daniel Moll Victor Hugo 2021 04 23 2014 10 06 Errata for Tables of Integrals Series and Products 8th edition by I S Gradshteyn and M Ryzhik edited by Daniel Zwillinger and Victor Moll Academic Press 2014 ISBN 0 12 384933 0 PDF 6 ed Archived PDF from the original on 2021 04 25 Retrieved 2021 12 26 NB This list of 33 pages has 191 entries External links editZwillinger Daniel Gradshteyn and Ryzhik Table of Integrals Series and Products Home Page Archived from the original on 2016 03 08 Retrieved 2016 03 08 Moll Victor Hugo List with the formulas and proofs in GR Archived from the original on 2010 01 09 Retrieved 2016 03 08 SCIENTIA Series A Mathematical Sciences Official Journal of the Universidad Tecnica Federico Santa Maria Universidad Tecnica Federico Santa Maria UTFSM Retrieved 2016 03 08 Blackley Jonathan Seamus 2021 06 12 2021 06 11 One of my most cherished things a tool so useful and powerful that I honesty have come to look at it as a friend Table of Integrals Series and Products twitter Archived from the original on 2021 09 11 Retrieved 2022 01 12 Retrieved from https en wikipedia org w index php title Gradshteyn and Ryzhik amp oldid 1177721568 Ryzhik, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.