This material has been published in
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.
Proof of a summation formula for an Ãn
basic hypergeometric series conjectured by Warnaar
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.
The following versions are available:
Back to Christian Krattenthaler's