Abstract
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.
Highlights
The history of the subject of this article started in 1964 when Srivastava [1] investigated the domain of convergence for the first two functions in this article
We continue our treatment from the book [5], where a reduction formula for a q-Lauricella function was presented
We first give the general reduction formula, we specify to triple functions
Summary
The history of the subject of this article started in 1964 when Srivastava [1] investigated the domain of convergence for the first two functions in this article (for q = 1) He obtained an Euler integral formula for HA and the predecessor of formula (58). To find Euler integral formulas for q-analogues of Srivastava’s triple hypergeometric functions.
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