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Proof of a summation formula for an $\tilde A_n$ basic hypergeometric series conjectured by Warnaar

Christian Krattenthaler
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Abstract

A proof of an unusual summation formula for a basic hypergeometric series associated to the affine root system $\tilde A_n$ that was conjectured by Warnaar is given. It makes use of Milne's $A_n$ extension of Watson's transformation, Ramanujan's $_1ψ_1$-summation, and a determinant evaluation of the author. In addition, a transformation formula between basic hypergeometric series associated to the affine root systems $\tilde A_n$ respectively $\tilde A_m$, 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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Christian Krattenthaler. 2002-09-20. Proof of a summation formula for an $\tilde A_n$ basic hypergeometric series conjectured by Warnaar. https://arxiv.org/abs/math/0209272

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