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arXiv · 0904.0561

A First Order $q$-Difference System for the $BC_1$-Type Jackson Integral and Its Applications

Masahiko Ito
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Abstract

We present an explicit expression for the $q$-difference system, which the $BC_1$-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.

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Masahiko Ito. 2009-04-03. A First Order $q$-Difference System for the $BC_1$-Type Jackson Integral and Its Applications. https://doi.org/10.3842/sigma.2009.041

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