English

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

Classical Analysis and ODEs 2007-05-23 v1

Abstract

A proof of an unusual summation formula for a basic hypergeometric series associated to the affine root system A~n\tilde A_n that was conjectured by Warnaar is given. It makes use of Milne's AnA_n extension of Watson's transformation, Ramanujan's 1ψ1_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 A~n\tilde A_n respectively A~m\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.

Keywords

Cite

@article{arxiv.math/0209272,
  title  = {Proof of a summation formula for an $\tilde A_n$ basic hypergeometric series conjectured by Warnaar},
  author = {Christian Krattenthaler},
  journal= {arXiv preprint arXiv:math/0209272},
  year   = {2007}
}

Comments

9 pages, AmS-LaTeX