Fock, V. A. (1943), "On the representation of an arbitrary function by an integral involving Legendre's functions with a complex index", C. R. (Doklady) Acad. Sci. URSS, New Series, 39: 253–256, MR 0009665
Mehler, F. G. (1881), "Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der Elektricitätsvertheilung", Mathematische Annalen (in German), Springer Berlin / Heidelberg, 18 (2): 161–194, doi:10.1007/BF01445847, ISSN 0025-5831
mehler, fock, transform, mathematics, integral, transform, introduced, mehler, 1881, rediscovered, fock, 1943, given, displaystyle, infty, quad, infty, where, legendre, function, first, kind, under, appropriate, conditions, following, inversion, formula, holds. In mathematics the Mehler Fock transform is an integral transform introduced by Mehler 1881 and rediscovered by Fock 1943 It is given by F x 0 P i t 1 2 x f t d t 1 x displaystyle F x int 0 infty P it 1 2 x f t dt quad 1 leq x leq infty where P is a Legendre function of the first kind Under appropriate conditions the following inversion formula holds f t t tanh p t 1 P i t 1 2 x F x d x 0 t displaystyle f t t tanh pi t int 1 infty P it 1 2 x F x dx quad 0 leq t leq infty References editBrychkov Yu A Prudnikov A P 2001 1994 Mehler Fock transform Encyclopedia of Mathematics EMS Press Fock V A 1943 On the representation of an arbitrary function by an integral involving Legendre s functions with a complex index C R Doklady Acad Sci URSS New Series 39 253 256 MR 0009665 Mehler F G 1881 Ueber eine mit den Kugel und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der Elektricitatsvertheilung Mathematische Annalen in German Springer Berlin Heidelberg 18 2 161 194 doi 10 1007 BF01445847 ISSN 0025 5831 Yakubovich S B 2001 1994 Mehler Fock transform Encyclopedia of Mathematics EMS Press Retrieved from https en wikipedia org w index php title Mehler Fock transform amp oldid 1014537732, wikipedia, wiki, book, books, library,
