This material has been published in "q-Series with Applications to Combinatorics, Number Theory, and Physics," Urbana-Champaign, Oct. 26-28, 2000, B. C. Berndt, K. Ono, eds., Contemporary Math., vol. 291, Amer. Math. Soc., Providence, R.I., 2001, pp. 153-161, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the American Mathematical Society. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler

Proof of a summation formula for an Ãn basic hypergeometric series conjectured by Warnaar

(9 pages)

Abstract. A proof of an unusual summation formula for a basic hypergeometric series associated to the affine root system Ãn that was conjectured by Warnaar is given. It makes use of Milne's An extension of Watson's transformation, Ramanujan's 1psi1-summation, and a determinant evaluation of the author. In addition, a transformation formula between basic hypergeometric series associated to the affine root systems Ãn respectively Ãn, 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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