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

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.

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

References in corpus (2)

• On certain multiple Bailey, Rogers and Dougall type summation formulas
• Elementary derivations of identities for bilateral basic hypergeometric series

Cited by in corpus (7)

• Another proof of Bailey's 6-psi-6 summation
• Elementary derivations of identities for bilateral basic hypergeometric series
• Some more semi-finite forms of bilateral basic hypergeometric series
• Generalized Ismail's argument and $(f,g)$-expansion formula
• Inversion of bilateral basic hypergeometric series
• The united proofs for three $q$-extensions of Dougall's ${}_2{H}_2$ summation formula
• Semi-Finite Forms of Bilateral Basic Hypergeometric Series