Weierstrass product representations of multiple gamma and sine functions
type: Item
instance of: scholarly article
title: Weierstrass product representations of multiple gamma and sine functions
zbMATH Open document ID: 1191.11023
author: Kazuhiro Onodera
published in: Kodai Mathematical Journal
publication date: 2009-05-18T00:00:00Z
review text: The paper deals with multiple gamma and sine functions. The Weierstrass product representations for multiple gamma function was obtained by Barnes, while \textit{N. Kurokawa} and \textit{S. Koyama} [``Multiple sine functions'', Forum Math. 15, No. 6, 839--876 (2003; Zbl 1065.11065)] gave the infinite product representation for multiple sine function. However, the two representations contain polynomials with unknown coefficients. In the special case of the multiple parameter \(\underline\omega=(1, ..., 1)\), the author fills this gap and presents the explicit formulas for these coefficients. Similar results also are given for the Vignéras multiple gamma function.
reviewed by: Renata Macaitienė
Mathematics Subject Classification ID: 11M35
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 33B10
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 33E20
zbMATH DE Number: 5554646
zbMATH Keywords: multiple Hurwitz zeta function
zbMATH Keywords: multiple gamma function
zbMATH Keywords: multiple sine function
zbMATH Keywords: Weierstrass product
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1238594547
OpenAlex ID: W2012015838
DOI: 10.2996/KMJ/1238594547
Recommended article: On products of Weierstrass sigma functions
Recommended article: Multiple gamma functions, multiple sine functions, and Appell's \(O\)-functions
Recommended article: Q2953426
Recommended article: Multiple gamma functions and \(L\)-functions
Recommended article: On the product of the gamma function and the Hurwitz zeta function
Recommended article: Q4343381
Recommended article: Q5172411
Recommended article: Multiple gamma functions and multiple \(q\)-gamma functions
Recommended article: Products of incomplete gamma functions
Recommended article: On the multiple gamma-functions
description: scientific article; zbMATH DE number 5554646