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Rational series for multiple zeta and log gamma functions
Authors:Paul Thomas Young
Institution:Department of Mathematics, College of Charleston, Charleston, SC 29424, USA
Abstract:

Text

We give series expansions for the Barnes multiple zeta functions in terms of rational functions whose numerators are complex-order Bernoulli polynomials, and whose denominators are linear. We also derive corresponding rational expansions for Dirichlet L-functions and multiple log gamma functions in terms of higher order Bernoulli polynomials. These expansions naturally express many of the well-known properties of these functions. As corollaries many special values of these transcendental functions are expressed as series of higher order Bernoulli numbers.

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Keywords:Barnes zeta functions  Hurwitz zeta function  Multiple zeta functions  Multiple gamma functions  Bernoulli polynomials  Dirichlet L-functions  Polygamma functions
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