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

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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

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

Acta Applicandae Mathematicae , Volume 86 (3) – Dec 9, 2004

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-004-7465-4
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Dec 9, 2004

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