## Michael J. Schlosser

# A simple proof of Bailey's very-well-poised
_{6}Ψ_{6}
summation

### (10 pages)

**Abstract.**
We give elementary derivations of some classical
summation formulae for bilateral (basic)
hypergeometric series. In particular, we
apply Gauß' _{2}Φ_{1} summation
and elementary series manipulations, to give a simple proof of
Dougall's _{2}H_{2} summation. Similarly, we apply
Rogers' nonterminating _{6}Φ_{5} summation
and elementary series manipulations to give a simple proof of Bailey's
very-well-poised _{6}Ψ_{6} summation.
Our method of proof extends M. Jackson's first elementary proof of
Ramanujan's _{1}Ψ_{1} summation.

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