Some Closed-Form Evaluations of Multiple Hypergeometric and <Emphasis Type="Italic">q</Emphasis>-Hypergeometric Series |
| |
Authors: | Email author" target="_blank">Shy-Der?LinEmail author H?M?Srivastava |
| |
Institution: | (1) Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, 32023, Taiwan, Republic of China;(2) Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3P4, Canada |
| |
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.
Dedicated to the Memory of Leonard Carlitz (1907–1999)Mathematics Subject Classifications (2000) Primary 33C65, 33C70, 33D70; secondary 33C20, 33D15. |
| |
Keywords: | multiple hypergeometric and q-hypergeometric series summation formulas reduction formulas Gamma function Pfaff– Saalschü tz theorem Gauss summation theorem Srivastava– Daoust multivariable hypergeometric function Appell and Lauricella series Kummer s theorem" target="_blank">gif" alt="rsquo" align="BASELINE" BORDER="0">s theorem linear transformations contiguous-function analogues Eulerian Beta-function integrals |
本文献已被 SpringerLink 等数据库收录! |
|