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

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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.
9 pages, AmS-LaTeX

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Classical Analysis and ODEs, 33D67 (Primary) 05A19 05A30 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/65019

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209272
 http://arxiv.org/abs/math/0209272
 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

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