ON THE BARNES MULTIPLE ZETA AND GAMMA FUNCTION
Author:


2010 Mathematics Subject Classification:

11M35, 11M41.

Keywords:

Hurwitz zetafunction, multiple gamma function, Stirling number.

Abstract:

We shall develop the theory of Barnes multiple zetafunction 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 function by which we may supplement [25p. 307], in which the general case is treated only up to (function). This allows us to convert sums involving Hurwitz zetafunction into the sums involving multiple gamma function, thus covering all possible formulas in this direction.

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Vol. 9 (17), 2014
