Michael J. Schlosser
Elementary derivations of identities for bilateral basic
We give elementary derivations of several classical and some new
summation and transformation formulae for bilateral basic
hypergeometric series. For purpose of motivation, we review
our previous simple proof of Bailey's
very-well-poised 6ψ6 summation.
Using a similar but different method,
we now give elementary derivations of some transformations for bilateral
basic hypergeometric series.
In particular, these include M. Jackson's very-well-poised
8ψ8 transformation, a very-well-poised
10ψ10 transformation, by induction,
Slater's general transformation for very-well-poised
2rψ2r series, and Slater's transformation
for general rψr series.
Finally, we derive some new transformations for bilateral
basic hypergeometric series of a specific type.
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