PERIOD DEFORMATIONS AND RAABE'S FORMULAS FOR GENERALIZED GAMMA AND SINE FUNCTIONS

Nobushige KUROKAWA; Masato WAKAYAMA

doi:10.2206/kyushujm.62.171

Kyushu Journal of Mathematics

Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116

PERIOD DEFORMATIONS AND RAABE'S FORMULAS FOR GENERALIZED GAMMA AND SINE FUNCTIONS

Nobushige KUROKAWA, Masato WAKAYAMA

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Keywords: multiple Hurwitz's zeta function, multiple gamma function; multiple sine, function, multiplication formulas, Raabe's formula

JOURNAL FREE ACCESS

2008 Volume 62 Issue 1 Pages 171-187

DOI https://doi.org/10.2206/kyushujm.62.171

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Abstract

Deformations of the multiple gamma and sine functions with respect to their periods are studied. To describe such deformations explicitly, a new class of generalized gamma and sine functions are introduced. In particular, we study the deformations from the viewpoint of multiplication formulas and Raabe's integral formulas for these gamma and sine functions. This new class of gamma functions contains Milnor's type multiple gamma functions as a special case.

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