The q-multiple gamma functions of Barnes-Milnor type

2019/05/16 by Kawamura, Hanamichi
#33B15 #33D05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.08068

Abstract

The multiple gamma functions of BM (Barnes-Milnor) type and the q-multiple gamma functions have been studied independently. In this paper, we introduce a new generalization of the multiple gamma functions called the q-BM multiple gamma function including those functions and prove some properties the BM multiple gamma functions satisfy for them.

Related

• Asymptotic Expansions for the multiple gamma functions of Barnes-Milnor type
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• Contributions to the Theory of the Barnes Function
• On the (p,q)-Gamma and the (p,q)-Beta functions
• The multiple gamma functions and the multiple q-gamma functions