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This article is cited in 1 scientific paper (total in 1 paper)
$q$-Difference Systems for the Jackson Integral of Symmetric Selberg Type
Masahiko Ito Department of Mathematical Sciences, University of the Ryukyus, Okinawa 903-0213, Japan
Abstract:
We provide an explicit expression for the first order $q$-difference system for the Jackson integral of symmetric Selberg type. The $q$-difference system gives a generalization of $q$-analog of contiguous relations for the Gauss hypergeometric function. As a basis of the system we use a set of the symmetric polynomials introduced by Matsuo in his study of the $q$-KZ equation. Our main result is an explicit expression for the coefficient matrix of the $q$-difference system in terms of its Gauss matrix decomposition. We introduce a class of symmetric polynomials called interpolation polynomials, which includes Matsuo's polynomials. By repeated use of three-term relations among the interpolation polynomials we compute the coefficient matrix.
Keywords:
$q$-difference equations, Selberg type integral, contiguous relations, Gauss decomposition.
Received: April 29, 2020; in final form October 29, 2020; Published online November 8, 2020
Citation:
Masahiko Ito, “$q$-Difference Systems for the Jackson Integral of Symmetric Selberg Type”, SIGMA, 16 (2020), 113, 31 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1651 https://www.mathnet.ru/eng/sigma/v16/p113
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Abstract page: | 48 | Full-text PDF : | 21 | References: | 10 |
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