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Special values of generalized log-sine integrals

Special values of generalized log-sine integrals
Jonathan M. Borwein, Armin Straub — Proceedings of ISSAC 2011 (International Symposium on Symbolic and Algebraic Computation) — 2011, Pages 43-50

It was my great honor to receive the ISSAC 2011 Distinguished Student Author award for this paper.

Mathematica package

The Mathematica package LsToLi is available for download; so is a preliminary package for Sage.

Abstract

We study generalized log-sine integrals at special values. At $$\pi$$ and multiples thereof explicit evaluations are obtained in terms of multiple polylogarithms at $$\pm1$$. For general arguments we present algorithmic evaluations involving polylogarithms at related arguments. In particular, we consider log-sine integrals at $$\pi/3$$ which evaluate in terms of polylogarithms at the sixth root of unity. An implementation of our results for the computer algebra systems Mathematica and Sage is provided.

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BibTeX

@article{logsin-issac-2011,
author = {Jonathan M. Borwein and Armin Straub},
title = {Special values of generalized log-sine integrals},
journal = {Proceedings of ISSAC 2011 (International Symposium on Symbolic and Algebraic Computation)},
year = {2011},
pages = {43--50},
doi = {10.1145/1993886.1993899},
}