Extensions of certain classical integrals of Erdelyi for Gauss hypergeometric functions

[摘要] It is shown how series manipulation technique and certain classical summation theorems for hypergeometric series can be used to prove Erdelyi's integral representations for F-2(1)(z), originally proved using fractional calculus. The method not only leads to generalizations but also leads to new integrals of Erdelyi type for certain F-q+1(q)(z) and corresponding Pochhammer contour integrals. The technique outlined here, compared to the method of fractional calculus, seems to be more effective as it not only provides transparent elementary proofs of Erdelyi's integrals but even leads to various generalizations. (C) 2003 Elsevier B.V. All rights reserved.

[发布日期] 2003-11-01

[效力级别]  Proceedings Paper

[关键词] hypergeometric functions;integrals;fractional calculus;series manipulation technique;classical summation theorems