Weierstrass product representations of multiple gamma and sine functions (Q1017350)

The paper deals with multiple gamma and sine functions. The Weierstrass product representations for multiple gamma function was obtained by Barnes, while \textit{N. Kurokawa} and \textit{S. Koyama} [``Multiple sine functions'', Forum Math. 15, No. 6, 839--876 (2003; Zbl 1065.11065)] gave the infinite product representation for multiple sine function. However, the two representations contain polynomials with unknown coefficients. In the special case of the multiple parameter \(\underline\omega=(1, ..., 1)\), the author fills this gap and presents the explicit formulas for these coefficients. Similar results also are given for the Vignéras multiple gamma function.