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Axioms 2013, 2(2), 85-99; doi:10.3390/axioms2020085
Article

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

Received: 28 February 2013 / Revised: 22 March 2013 / Accepted: 3 April 2013 / Published: 11 April 2013
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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.
Keywords: Euler integral formula; summation and reduction formula; q-integral Euler integral formula; summation and reduction formula; q-integral
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.

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Ernst, T. On the q-Analogues of Srivastava’s Triple Hypergeometric Functions. Axioms 2013, 2, 85-99.

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