Talk: Symbolic evaluation of log-sine integrals in polylogarithmic terms (JMM)

Date: 2012/01/07
Occasion: AMS Joint Meetings 2012
Place: Boston

This talk, given at the AMS Joint Meetings 2012 in Boston, basically is a short version of the talk given at ISSAC 2011 and presents results of the paper Special values of generalized log-sine integrals together with a brief indication of two applications of log-sine integrals (Mahler measure and inverse binomial sums).

Abstract

Generalized log-sine integrals, first studied systematically by Lewin 50 years ago, appear in many settings in number theory and analysis: for instance, they can be used to express classes of inverse binomial sums. As such they have reappeared in recent work on the epsilon-expansion of Feynman diagrams in physics; they have also proved useful in the study of certain multiple Mahler measures. We sketch these developments and present results which allow for the symbolic computation of log-sine integrals in terms of Nielsen polylogarithms at related argument. In particular, log-sine integrals at pi/3 are shown to evaluate in terms of polylogarithms at the sixth root of unity.

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