PROOF OF A SUMMATION FORMULA FOR AN Ãn BASIC HYPERGEOMETRIC SERIES CONJECTURED BY WARNAAR
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چکیده
Abstract. A proof of an unusual summation formula for a basic hypergeometric series associated to the affine root system Ãn that was conjectured byWarnaar is given. It makes use of Milne’s An extension of Watson’s transformation, Ramanujan’s 1ψ1summation, and a determinant evaluation of the author. In addition, a transformation formula between basic hypergeometric series associated to the affine root systems Ãn respectively Ãm, 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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تاریخ انتشار 2002