Michael J. Schlosser
A simple proof of Bailey's very-well-poised
6Ψ6
summation
(10 pages)
Abstract.
We give elementary derivations of some classical
summation formulae for bilateral (basic)
hypergeometric series. In particular, we
apply Gauß' 2Φ1 summation
and elementary series manipulations, to give a simple proof of
Dougall's 2H2 summation. Similarly, we apply
Rogers' nonterminating 6Φ5 summation
and elementary series manipulations to give a simple proof of Bailey's
very-well-poised 6Ψ6 summation.
Our method of proof extends M. Jackson's first elementary proof of
Ramanujan's 1Ψ1 summation.
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