A simple proof of Bailey's very-well-poised 6-psi-6 summation
Classical Analysis and ODEs
2019-02-22 v2 Combinatorics
Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0007046,
title = {A simple proof of Bailey's very-well-poised 6-psi-6 summation},
author = {M. Schlosser},
journal= {arXiv preprint arXiv:math/0007046},
year = {2019}
}
Comments
LaTeX2e, 10 pages, submitted to Proc. AMS, revised version, proofs of 1-psi-1 and 2-H-2 summations included