Special values of generalized log-sine integrals
- 8 June 2011
- conference paper
- conference paper
- Published by Association for Computing Machinery (ACM) in Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11
Abstract
We study generalized log-sine integrals at special values. At π and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at ±1. For general arguments we present algorithmic evaluations involving Nielsen polylogarithms at related arguments. In particular, we consider log-sine integrals at π/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 providedKeywords
This publication has 20 references indexed in Scilit:
- On multiple higher Mahler measures and multiple L valuesActa Arithmetica, 2010
- Higher Mahler measures and zeta functionsActa Arithmetica, 2008
- HPL, a Mathematica implementation of the harmonic polylogarithmsComputer Physics Communications, 2006
- lsjk—a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functionsComputer Physics Communications, 2005
- Numerical evaluation of multiple polylogarithmsComputer Physics Communications, 2005
- Single-scale diagrams and multiple binomial sumsPhysics Letters B, 2000
- On the series Σk = 1∞(k2k)−1k−n and related sumsJournal of Number Theory, 1985
- Closed Expressions for 1 0 t -1 log n-1 t log p (1 - t) dtMathematics of Computation, 1982
- Speculations Concerning the Range of Mahler's MeasureCanadian Mathematical Bulletin, 1980
- 4917The American Mathematical Monthly, 1961