Michael J. Schlosser
A simple proof of Bailey's very-well-poised
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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