Some Closed-Form Evaluations of Multiple Hypergeometric and q-Hypergeometric Series

The main object of the present paper is to show how some fairly general analytical tools and techniques can be applied with a view to deriving summation, transformation and reduction formulas for multiple hypergeometric and multiple basic (or q-) hypergeometric series. By making use of some reductio...

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Bibliographic Details
Published in:Acta applicandae mathematicae Vol. 86; no. 3; pp. 309 - 327
Main Authors: Lin, Shy-Der, Srivastava, H. M.
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.05.2005
Subjects:
Geometry
Mathematical analysis
Studies
ISSN:0167-8019, 1572-9036
Online Access:Get full text
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Summary:The main object of the present paper is to show how some fairly general analytical tools and techniques can be applied with a view to deriving summation, transformation and reduction formulas for multiple hypergeometric and multiple basic (or q-) hypergeometric series. By making use of some reduction formulas for multivariable hypergeometric functions, the authors investigate several closed-form evaluations of various families of multiple hypergeometric and q-hypergeometric series. Relevant connections of the results presented in this paper with those obtained in earlier works are also considered. A number of multiple q-series identities, which are developed in this paper, are observed to be potentially useful in the related problems involving closed-form evaluations of multivariable q-hypergeometric functions. [PUBLICATION ABSTRACT]
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-004-7465-4