On a theta product formula for Jackson integrals associated with root systems of rank two
type: Item
instance of: scholarly article
title: On a theta product formula for Jackson integrals associated with root systems of rank two
zbMATH Open document ID: 0902.33011
author: Masahiko Ito
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-12-06T00:00:00Z
review text: The classical Selberg integral, which appears in the random matrix theory, possesses the symmetry with respect to a group \(S_n\) and can be expressed as the product of gamma functions. Analogous integrals, associated with root systems are also expressed in the same way. The present paper is devoted to the study of \(q\)-analogues of Selberg integrals associated with root systems which are called the Jackson integrals of Selberg type. The author conjectures the formula for calculating these integrals as the product of \(q\)-gamma functions and Jacobi elliptic theta functions (the theta product formula). This formula is proved for root systems of rank two.
Mathematics Subject Classification ID: 33D05
Mathematics Subject Classification ID: 33D10
Mathematics Subject Classification ID: 33D80
zbMATH DE Number: 1115527
zbMATH Keywords: Selberg integral
zbMATH Keywords: Jackson integral
zbMATH Keywords: \(q\)-gamma function
zbMATH Keywords: Jacobi theta function
reviewed by: Michael Kuznetsov
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5665
OpenAlex ID: W1996902840
cites work: q-identities of Auluck, Carlitz, and Rogers
cites work: q-analogue of de Rham cohomology associated with Jackson integrals. I
cites work: On Connection Coefficients forq-Difference Systems ofA-Type Jackson Integrals
cites work: Connection formula of symmetric \(A\)-type Jackson integrals
cites work: Q4000402
cites work: Variation on a theme of Macdonald
cites work: Multidimensional q-Beta Integrals
cites work: A Beta Integral Associated with the Root System $G_2 $
cites work: Une q-Intégrale de Selberg et Askey
cites work: A Proof of Askey’s Conjectured q-Analogue of Selberg’s Integral and a Conjecture of Morris
cites work: A proof of the 𝑞-Macdonald-Morris conjecture for 𝐵𝐶_{𝑛}
cites work: $q$-Selberg integrals and Macdonald polynomials
cites work: Some Conjectures for Root Systems
cites work: Q3725277
cites work: Some applications of hypergeometric shift operators
cites work: Q4440598
cites work: On certain multiple Bailey, Rogers and Dougall type summation formulas
DOI: 10.1006/JMAA.1997.5665
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description: scientific article; zbMATH DE number 1115527