Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 712321, 14 pages
http://dx.doi.org/10.1155/2014/712321
Research Article

Decomposition Formulas for Triple -Hypergeometric Functions

Department of Mathematics, Uppsala University, P.O. Box 480, SE-751 06 Uppsala, Sweden

Received 11 November 2013; Accepted 31 December 2013; Published 15 May 2014

Academic Editor: R. Yuster

Copyright © 2014 Thomas Ernst. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the spirit of Hasanov, Srivastava, and Turaev (2006), we introduce new inverse operators together with a more general operator and find a summation formula for the last one. Based on these operators and the earlier known -analogues of the Burchnall-Chaundy operators, we find 15 symbolic operator formulas. Then, 10 expansions for the -analogues of Srivastava’s three triple hypergeometric functions in terms of -hypergeometric and -Kampé de Fériet functions are derived. These expansions readily reduce to 10 new expansions for the three triple Srivastava hypergeometric functions in terms of hypergeometric and Kampé de Fériet functions.