Some reduction and transformation formulas for the Appell hypergeometric function F2

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:302

Article

Opps, SB ; Saad, N ; Srivastava, HM

关键词: multiple hypergeometric functions;    Appell series;    integral representations;    singular potentials;    Gordon's integral;    Gauss hypergeometric function;    Clausen hypergeometric function;    Kummer (or confluent) hypergeometric function;    reduction and transformation formulas;    singular operators;    dilogarithm function;    digamma (or Psi) function;   

DOI  :  10.1016/j.jmaa.2004.07.052

来源: Elsevier

【 摘 要 】

An integral representation of the Appell series F-2(sigma,alpha(1),alpha(2);beta(1), beta(2); x, y) is used here to obtain several finite-sum expansions in terms of the less cumbersome hypergeometric functions F-2(1) and F-3(2). In the case when the parameters sigma, alpha(1), alpha(2), beta(1), and beta(2) are all positive integers, some of our results may be seen as a generalization of the finite-sum expansions of the Appell series F-1 obtained by Cuyt et al. Other important consequences (as well as potential applications) of our results are discussed and a listing of some useful reduction (and transformation) formulas is provided. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free