On a q-Analogue of the Multiple Gamma Function

@

Author

Michitomo Nishizawa

Journal

Lett.Math.Phys. 33 (1996), 201-208,

Abstract

A q-analogue of multiple gamma function is constructed. This function satisfies a q-analogue of the Bohr-Morellup theorem. Furthermore, infinite product representations are derived.

Cited by:

S. Koshkin
Quantum Barnes function as the partition function of the resolved conifold
arXiv:0710.2929v1 [math.AG]

A. Narukawa,
The Modular Properties and the Integral Representations of the Multtiple Elliptic Gamma Functions,
Adv. Maths., 189(2004) 247-267. A mathQA/0306164

M. Nishizawa,
An Elliptic Analogue of the Multiple Gamma Function,
J. Phys. A : Math. Gen. 34 (2001), 7411-7421.

M. Nishizawa,
Multiple Gamma Function and Its q- and Elliptic Analogues,
Rockey Mount. J. Math. 32 (2002), 793-811

M. Nishizawa,
Infinite Product Representations for Multiple Gamma Function,
Preprint,@ mathCA/0404077.

S.N.M. Ruijsenaars,
A Generalized Hypergeometric Function Satisfying Four Analytic Difference Equations of Askey-Wilson type,
Comm. Math. Phys. 206 (1999), 639-690.

S.N.M. Ruijsenaars,
On Barns' Multiple Zeta and Gamma Functions,
Adv.Math. 156 (2000), 107-132.

K.Ueno and M. Nishizawa,
The Multiple Gamma Functions and the Multiple q-Gamma Functions,
Publ. RIMS. Kyoto Univ 33 (1997)