Multiple Gamma Functions and Their Applications

On Multiple Zeta Function and Associated Properties

“…[3][4][5][6][7][8][9][10][11][12][13][14]. The present sequel to these earlier papers is motivated largely by the aforementioned works of Matsumoto and Kamano [15,16] In the present paper we introduce a new class of zeta functions ( )…”

Pick functions related to the triple Gamma function

“…Using (2.1), the following explicit form of the multiple Gamma function of order n, in terms of Weierstrass canonical product of Γ n , is given in [12].…”

“…We remark that equivalent forms of Γ(z) exist in the literature, (see [12] for details). By defining Γ n (z) = (G n (z)) (−1) n−1 , n ∈ N.…”

Inequalities Involving $q$-Analogue of Multiple Psi Functions

“…The multiple gamma functions of Barnes [4,5] introduced more than a century ago have been taken up during the last decades because they enter in several different areas of modern mathematics represented by e.g., S. N. M. Ruijsenaars [13] and M. F. Vignéras [16]. These functions are useful in summation of series and infinite products and in the theory of elliptic functions and theta functions [7]. The inverse of the double gamma function is the well known G-function [7].…”