Elementary derivations of identities for bilateral basic hypergeometric series

Abstract

We give elementary derivations of several classical and some new summation and transformation formulae for bilateral basic hypergeometric series. For purpose of motivation, we review our previous simple proof ("A simple proof of Bailey's very-well-poised 6-psi-6 summation", Proc. Amer. Math. Soc., to appear) of Bailey's very-well-poised 6-psi-6 summation. Using a similar but different method, we now give elementary derivations of some transformations for bilateral basic hypergeometric series. In particular, these include M. Jackson's very-well-poised 8-psi-8 transformation, a very-well-poised 10-psi-10 transformation, by induction, Slater's general transformation for very-well-poised 2r-psi-2r series, and Slater's transformation for general r-psi-r series. Finally, we derive some new transformations for bilateral basic hypergeometric series of Chu-Gasper-Karlsson-Minton-type.

LaTeX2e, 35 pages, revised abstract and introduction

References in corpus (2)

• On certain multiple Bailey, Rogers and Dougall type summation formulas
• A simple proof of Bailey's very-well-poised 6-psi-6 summation

Cited by in corpus (5)

• A simple proof of Bailey's very-well-poised 6-psi-6 summation
• On the equivalence of two fundamental theta identities
• On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series
• A nonterminating 8-phi-7 summation for the root system C_r
• Inversion of bilateral basic hypergeometric series