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

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Cited by in corpus (5)

• The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction
• On logarithmic integrals, harmonic sums and variations
• Log-sine evaluations of Mahler measures, II
• The Fourier series of the log-Barnes function
• Contour integration underlies fundamental Bernoulli number recurrence