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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},
}
Date: 2011/03/23
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