ON THE BARNES MULTIPLE ZETA- AND GAMMA FUNCTION

Author:

Kalyan~Chakraborty,~Shigeru~Kanemitsu,~Takako~Kuzumaki

2010 Mathematics Subject Classification:

11M35, 11M41.

Keywords:

Hurwitz zeta-function, multiple gamma function, Stirling number.

Abstract:

We shall develop the theory of Barnes multiple zeta-func-tion from a slightly different point of view using the Norlund generalized Bernoulli polynomials and apply it to the integral of the multiple gamma function. We will provide  explicit formula for </span><span style="font-size: 1em; line-height: 1.3em;">\log \Gamma_3-function by which we may supplement [25p. 307], in which the general case is treated only up to r=2 (G-function). This allows us to convert sums involving Hurwitz zeta-function into the sums involving multiple gamma function, thus covering all possible formulas in this direction.

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Vol. 9 (17), 2014