Special Values of Generalized Log-sine Integrals

Abstract

We study generalized log-sine integrals at special values. At $\pi$ and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at $\pm 1$. For general arguments we present algorithmic evaluations involving Nielsen 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.

8 pages, to be published in the proceedings of ISSAC 2011

References in corpus (1)

• Log-sine evaluations of Mahler measures, II

Cited by in corpus (1)

• Log-sine evaluations of Mahler measures, II