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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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
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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.
AbstractList 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.
Author Ernst, Thomas
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Cites_doi 10.1007/BF02844089
10.1007/978-3-0348-0431-8
10.1515/dema-2013-0317
10.1016/j.jmaa.2006.01.006
10.11650/twjm/1500406495
10.1007/BF02849368
10.7146/math.scand.a-11526
10.1093/qmath/os-13.1.69
10.2991/jnmp.2003.10.4.5
10.3176/proc.2008.2.03
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Snippet We find Euler integral formulas, summation and reduction formulas for q-analogues of Srivastava’s three triple hypergeometric functions. The proofs use...
We find Euler integral formulas, summation and reduction formulas for q-analogues of Srivastava's three triple hypergeometric functions. The proofs use...
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SubjectTerms Euler integral formula
q-integral
summation and reduction formula
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