English

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