
SIGMA 5 (2009), 041, 14 pages arXiv:0904.0561
https://doi.org/10.3842/SIGMA.2009.041
Contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions”
A First Order qDifference System for the BC_{1}Type Jackson Integral and Its Applications
Masahiko Ito
Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 2298558, Japan
Received December 01, 2008, in final form March 18, 2009; Published online April 03, 2009
Abstract
We present an explicit expression for the qdifference system,
which the BC_{1}type Jackson integral (qseries) satisfies,
as first order simultaneous qdifference 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 qintegral introduced by NassrallahRahman and Gustafson.
Key words:
qdifference equations; Jackson integral of type BC_{1}; Gustafson's C_{n}type sum; NassrallahRahman integral.
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