Mathematics – Classical Analysis and ODEs
Scientific paper
2002-09-20
in: "q-Series with Applications to Combinatorics, Number Theory, and Physics," Urbana-Champaign, Oct. 26-28, 2000, B. C. Bernd
Mathematics
Classical Analysis and ODEs
9 pages, AmS-LaTeX
Scientific paper
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 $_1\psi_1$-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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