Lommel, Eugen von (1871), "Zur Theorie der Bessel'schen Functionen", Mathematische Annalen, 4 (1), Berlin / Heidelberg: Springer: 103–116, doi:10.1007/BF01443302
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lommel, polynomial, introduced, eugen, lommel, 1871, polynomial, giving, recurrence, relation, displaystyle, displaystyle, where, bessel, function, first, kind, they, given, explicitly, displaystyle, frac, gamma, gamma, also, editlommel, function, neumann, pol. A Lommel polynomial Rm n z introduced by Eugen von Lommel 1871 is a polynomial in 1 z giving the recurrence relation Jm n z Jn z Rm n z Jn 1 z Rm 1 n 1 z displaystyle displaystyle J m nu z J nu z R m nu z J nu 1 z R m 1 nu 1 z where Jn z is a Bessel function of the first kind They are given explicitly by Rm n z n 0 m 2 1 n m n G n m n n m 2n G n n z 2 2n m displaystyle R m nu z sum n 0 m 2 frac 1 n m n Gamma nu m n n m 2n Gamma nu n z 2 2n m See also editLommel function Neumann polynomialReferences editErdelyi Arthur Magnus Wilhelm Oberhettinger Fritz Tricomi Francesco G 1953 Higher transcendental functions Vol II PDF McGraw Hill Book Company Inc New York Toronto London MR 0058756 Ivanov A B 2001 1994 Lommel polynomial Encyclopedia of Mathematics EMS Press Lommel Eugen von 1871 Zur Theorie der Bessel schen Functionen Mathematische Annalen 4 1 Berlin Heidelberg Springer 103 116 doi 10 1007 BF01443302 nbsp This polynomial related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Lommel polynomial amp oldid 1170027708, wikipedia, wiki, book, books, library,