Proof of a summation formula for an An basic hypergeometric series conjectured by Warnaar
Abstract
A proof of an unusual summation formula for a basic hypergeometric series associated to the affine root system An that was conjectured by Warnaar is given. It makes use of Milne's An extension of Watson's transformation, Ramanujan's 11-summation, and a determinant evaluation of the author. In addition, a transformation formula between basic hypergeometric series associated to the affine root systems An respectively Am, which generalizes at the same time the above summation formula and an identity due to Gessel and the author, is proposed as a conjecture.
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