Special Values of Generalized Log-sine Integrals

Details Special Values of Generalized Log-sine Integrals Special Values of Generalized Log-sine Integrals

2011-03-22

arxiv.org/abs/1103.4298v1

Mathematics

Classical Analysis and ODEs

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

Scientific paper

We study generalized log-sine integrals at special values. At $\pi$ and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at $\pm1$. 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.

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