Kodai Mathematical Journal

Weierstrass product representations of multiple gamma and sine functions

Kazuhiro Onodera

Full-text: Open access

Abstract

It is well known that the Weierstrass product representation of the Barnes multiple gamma function Γr(z) can be calculated concretely. However, there has been no study on its explicit formulation. In this paper, its simple formulation is achieved. It is applicable to the Weierstrass product representation of the Vignéras multiple gamma function also. Moreover, the Weierstrass product representation of the Kurokawa multiple sine function Sr(z) is also formulated explicitly.

Article information

Source
Kodai Math. J., Volume 32, Number 1 (2009), 77-90.

Dates
First available in Project Euclid: 1 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1238594547

Digital Object Identifier
doi:10.2996/kmj/1238594547

Mathematical Reviews number (MathSciNet)
MR2518555

Zentralblatt MATH identifier
1191.11023

Citation

Onodera, Kazuhiro. Weierstrass product representations of multiple gamma and sine functions. Kodai Math. J. 32 (2009), no. 1, 77--90. doi:10.2996/kmj/1238594547. https://projecteuclid.org/euclid.kmj/1238594547


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