期刊
ADVANCES IN MATHEMATICS
卷 189, 期 2, 页码 247-267出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2003.11.009
关键词
modular property; multiple elliptic gamma function; multiple sine function; q-shifted factorial; generalized q-polylogarithm
类别
We show the modular properties of the multiple elliptic gamma functions, which are an extension of those of the theta function and the elliptic gamma function. The modular property of the theta function is known as Jacobi's transformation, and that of the elliptic gamma function was provided by Felder and Varchenko. In this paper, we deal with the multiple sine functions, since the modular properties of the multiple elliptic gamma functions result from the equivalence between two ways to represent the multiple sine functions as infinite products. We also derive integral representations of the multiple sine functions and the multiple elliptic gamma functions. We introduce correspondences between the multiple elliptic gamma functions and the multiple sine functions. (C) 2003 Elsevier Inc. All rights reserved.
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