A theta product formula for Jackson integrals associated with root systems
type: Item
instance of: scholarly article
title: A theta product formula for Jackson integrals associated with root systems
zbMATH Open document ID: 0882.33011
author: Masahiko Ito
published in: Proceedings of the Japan Academy. Series A
publication date: 1998-02-15T00:00:00Z
review text: Jackson integrals \(J_R(k,\overline{\xi})\) associated with irreducible reduced root system \(R\) are defined. The formula expressing \(J_R(k,\overline{\xi})\) as the product on \(\alpha \in R^+\) of q-gamma functions and Jacobi elliptic theta functions depending on \(\alpha \) is conjectured. The result according to which this formula is true for \(R\) of type \(A_n, B_2, G_2\) is announced. For these cases the explicit theta product formulas are given.
Mathematics Subject Classification ID: 33D05
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 33D70
Mathematics Subject Classification ID: 33D10
Mathematics Subject Classification ID: 33D60
Mathematics Subject Classification ID: 33D80
zbMATH DE Number: 1057079
zbMATH Keywords: Jackson integral
zbMATH Keywords: theta function
zbMATH Keywords: q-gamma function
zbMATH Keywords: root system
reviewed by: Michael Kuznetsov
MaRDI profile type: Publication
full work available at URL: pjaa.73.60
OpenAlex ID: W2045224215
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DOI: 10.3792/PJAA.73.60
description: scientific article; zbMATH DE number 1057079