Special Values of Generalized Log-sine Integrals

Jonathan M. Borwein; Armin Straub

Special Values of Generalized Log-sine Integrals

Classical Analysis and ODEs 2011-03-23 v1 Symbolic Computation Mathematical Physics math.MP

Authors: Jonathan M. Borwein , Armin Straub

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 $\pm1$ . 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.

Keywords

matrix algorithms pi computation stochastic integrals

Cite

@article{arxiv.1103.4298,
  title  = {Special Values of Generalized Log-sine Integrals},
  author = {Jonathan M. Borwein and Armin Straub},
  journal= {arXiv preprint arXiv:1103.4298},
  year   = {2011}
}

Comments

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

Special Values of Generalized Log-sine Integrals

Abstract

Keywords

Cite

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