Special values of generalized log-sine integrals

This article by Jonathan M. Borwein and Armin Straub has been published in Proceedings of ISSAC 2011 .

You can also find this article on the arXiv as 1103.4298v1 [math.CA].

We study generalized log-sine integrals at special values. At π and multiples thereof explicit evaluations are obtained in terms of multiple polylogarithms at . For general arguments we present algorithmic evaluations involving polylogarithms at related arguments. In particular, we consider log-sine integrals at π/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.

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

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

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logsin-evaluations.pdf