Elementary derivations of identities for bilateral basic hypergeometric series

Details Elementary derivations of identities for bilateral basic hypergeometric series Elementary derivations of identities for bilateral basic hypergeometric series

2000-10-16

arxiv.org/abs/math/0010161v2

Mathematics

Classical Analysis and ODEs

LaTeX2e, 35 pages, revised abstract and introduction

Scientific paper

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.

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