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

2002/09/20 by Christian Krattenthaler
Mathematics · #math.CA #msc:33D67 #msc:05A19 #msc:05A30

paper · pdf

published as 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 · 9 pages, AmS-LaTeX

arxiv created 2002/09/20 · arxiv updated 2009/11/30

Abstract

A proof of an unusual summation formula for a basic hypergeometric series associated to the affine root system A_n that was conjectured by Warnaar is given. It makes use of Milne's A_n extension of Watson's transformation, Ramanujan's ₁ψ₁-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 respectively 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.

Related

• An Entry of Ramanujan on Hypergeometric Series in his Notebooks
• Factorization of Basic Hypergeometric Series
• Several transformation formulas for basic hypergeometric series
• Expansion formulas for multiple basic hypergeometric series over root systems
• Nonterminating Basic Hypergeometric Series and the q-Zeilberger Algorithm