MULTIPLE GAMMA FUNCTION,
ITS $q$- AND ELLIPTIC ANALOGUE

MICHITOMO NISHIZAWA

Abstract:

Vignéras's multiple gamma function is introduced as a function satisfying a generalization of the Bohr-Mollerup theorem. An infinite product representation and an asymptotic expansion of the function are given. Furthermore, its $q$- and elliptic analogue are introduced as relevant with the defining relations of $q$-gamma function and of elliptic gamma function.