Transformation formulas for bilinear sums of basic hypergeometric series

DOI10.4153/CMB-2015-016-8zbMATH Open1332.33023arXiv1310.7676MaRDI QIDQ2788797

Yasushi Kajihara

Publication date: 22 February 2016

Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)

Abstract: A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic hypergeometric series of type $A$ with different dimensions and it can be considered as a generalization of Whipple-Sears transformation formula for terminating balanced ${}_{4}ph{i}_3$ series. As an application of the master formula, one variable cases of some transformation formulas for bilinear sums of basic hypergeometric series are given as examples. The bilinear transformation formulas seem to be new in the literature even in one variable case.

Full work available at URL: https://arxiv.org/abs/1310.7676

zbMATH Keywords

basic hypergeometric seriesbilinear sums

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

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Title not available (Why is that?) ⋮ Title not available (Why is that?) ⋮ Duality transformation formulas for multiple elliptic hypergeometric series of type \(BC\) ⋮ Transformations from bilateral basic hypergeometric to unilateral basic hypergeometric series ⋮ A simple proof of W. N. Bailey's \({}_2\psi_2\) bilateral basic hypergeometric series transformation formula

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