A new An extension of Ramanujan's
summation with applications to multilateral
In this article, we derive some identities for multilateral basic
hypergeometric series associated to the root system An.
First, we apply Ismail's
argument to an An q-binomial theorem of
and derive a new An generalization of Ramanujan's
1ψ1 summation theorem.
From this new An 1ψ1
summation and from an An
1ψ1 summation of Gustafson
we deduce two lemmas for deriving simple An
bilateral basic hypergeometric series identities. These lemmas are
closely related to the Macdonald identities for An.
As samples for possible applications of these lemmas, we provide several
An extensions of Bailey's
and several An extensions of a particular
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