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Acta Applicandae Mathematica

, Volume 86, Issue 3, pp 309–327 | Cite as

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

  • Shy-Der LinEmail author
  • H. M. Srivastava
Article

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.

Keywords

multiple hypergeometric and q-hypergeometric series summation formulas reduction formulas Gamma function Pfaff–Saalschütz theorem Gauss summation theorem Srivastava–Daoust multivariable hypergeometric function Appell and Lauricella series Kummer’s theorem linear transformations contiguous-function analogues Eulerian Beta-function integrals 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Applied MathematicsChung Yuan Christian UniversityChung-LiTaiwan, Republic of China
  2. 2.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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