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,
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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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