On the q-Analogues of Srivastava’s Triple Hypergeometric Functions

We find Euler integral formulas, summation and reduction formulas for q-analogues of Srivastava’s three triple hypergeometric functions. The proofs use q-analogues of Picard’s integral formula for the first Appell function, a summation formula for the first Appell function based on the Bayley–Daum f...

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Bibliographic Details
Published in:	Axioms Vol. 2; no. 2; pp. 85 - 99
Main Author:	Ernst, Thomas
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01.06.2013
Subjects:	Euler integral formula q-integral summation and reduction formula
ISSN:	2075-1680, 2075-1680
Online Access:	Get full text
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Summary:	We find Euler integral formulas, summation and reduction formulas for q-analogues of Srivastava’s three triple hypergeometric functions. The proofs use q-analogues of Picard’s integral formula for the first Appell function, a summation formula for the first Appell function based on the Bayley–Daum formula, and a general triple series reduction formula of Karlsson. Many of the formulas are purely formal, since it is difficult to find convergence regions for these functions of several complex variables. We use the Ward q-addition to describe the known convergence regions of q-Appell and q-Lauricella functions.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	2075-1680 2075-1680
DOI:	10.3390/axioms2020085