Multiple Gamma Functions and Multiple $q$-Gamma Functions

Kimio Ueno; Michitomo Nishizawa

doi:10.2977/prims/1195145019

JournalsprimsVol. 33, No. 5pp. 813–838

Multiple Gamma Functions and Multiple $q$ -Gamma Functions

Kimio Ueno
Waseda University, Tokyo, Japan
- zbMATH Open
Michitomo Nishizawa
Waseda University, Tokyo, Japan
- MathSciNet
- zbMATH Open

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Abstract

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass canonical product representation) of the Vigneras multiple gamma functions by considering the classical limit of the multiple $q$ -gamma functions.

Cite this article

Kimio Ueno, Michitomo Nishizawa, Multiple Gamma Functions and Multiple $q$ -Gamma Functions. Publ. Res. Inst. Math. Sci. 33 (1997), no. 5, pp. 813–838

DOI 10.2977/PRIMS/1195145019