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VOL. 76 | 2018 A unified approach to transformations for multiple basic hypergeometric series of type $A$
Yasushi Kajihara

Editor(s) Hitoshi Konno, Hidetaka Sakai, Junichi Shiraishi, Takao Suzuki, Yasuhiko Yamada

Abstract

We propose a unified approach to transformation and summation formulas for multiple basic hypergeometric series of type $A$ on the basis of balanced duality transformations. We study two classes of transformations, one between an $n$-ple sum and an $m$-ple sum, and the other between two $n$-ple sums. Though the latter are not simple special cases of the former, we can still derive them from the former in a systematic way. Our derivation utilizes the fact that some multiple basic hypergeometric series have hidden symmetry which originates from the relation to basic hypergeometric series in one variable. We also give remarks on the related summation formulas.

Information

Published: 1 January 2018
First available in Project Euclid: 21 September 2018

zbMATH: 07039305
MathSciNet: MR3837924

Digital Object Identifier: 10.2969/aspm/07610247

Subjects:
Primary: 33D67
Secondary: 33D15, 33D20

Rights: Copyright © 2018 Mathematical Society of Japan

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