Rational series for multiple zeta and log gamma functions |
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Authors: | Paul Thomas Young |
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Institution: | Department of Mathematics, College of Charleston, Charleston, SC 29424, USA |
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Abstract: | TextWe 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.VideoFor a video summary of this paper, please click here or visit http://youtu.be/2i5PQiueW_8. |
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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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