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An elliptic analogue of the multiple gamma function. (English) Zbl 0993.33016

The author introduces an elliptic analogue of Barnes’s multiple gamma function, which generalizes the elliptic gamma function of S. N. M. Ruijsenaars [J. Math. Phys. 38, No. 2, 1069-1146 (1997; Zbl 0877.39002)]. The fundamental properties of this function are given.

MSC:

33E05 Elliptic functions and integrals
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)

Citations:

Zbl 0877.39002
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