Rational series for multiple zeta and log gamma functions

Abstract

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. For a video summary of this paper, please click here or visit http://youtu.be/2i5PQiueW_8 . Author Video Watch what authors say about their articles