Curious extensions of Ramanujan's
1Ψ1
summation formula
(12 pages)
Abstract.
We deduce new q-series identities by applying inverse
relations to certain identities for basic hypergeometric series.
The identities obtained themselves do not belong to the hierarchy
of basic hypergeometric series. We extend two of our identities,
by analytic continuation, to bilateral summation formulae which
contain Ramanujan's 1Ψ1 summation and a
very-well-poised 4Ψ6 summation as
special cases.
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