Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 041, 14 pages      arXiv:0904.0561
Contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions”

A First Order q-Difference System for the BC1-Type Jackson Integral and Its Applications

Masahiko Ito
Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 229-8558, Japan

Received December 01, 2008, in final form March 18, 2009; Published online April 03, 2009

We present an explicit expression for the q-difference system, which the BC1-type Jackson integral (q-series) satisfies, as first order simultaneous q-difference equations with a concrete basis. As an application, we give a simple proof for the hypergeometric summation formula introduced by Gustafson and the product formula of the q-integral introduced by Nassrallah-Rahman and Gustafson.

Key words: q-difference equations; Jackson integral of type BC1; Gustafson's Cn-type sum; Nassrallah-Rahman integral.

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