A simple proof of Bailey's very-well-poised 6-psi-6 summation

Details A simple proof of Bailey's very-well-poised 6-psi-6 summation A simple proof of Bailey's very-well-poised 6-psi-6 summation

2000-07-08

arxiv.org/abs/math/0007046v2

Mathematics

Classical Analysis and ODEs

LaTeX2e, 10 pages, submitted to Proc. AMS, revised version, proofs of 1-psi-1 and 2-H-2 summations included

Scientific paper

We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauss' 2-F-1 summation and elementary series manipulations to give a simple proof of Dougall's 2-H-2 summation. Similarly, we apply Rogers' nonterminating 6-phi-5 summation and elementary series manipulations to give a simple proof of Bailey's very-well-poised 6-psi-6 summation. Our method of proof extends M. Jackson's first elementary proof of Ramanujan's 1-psi-1 summation.

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