Special values of generalized log-sine integrals | Zendy

Jonathan M. Borwein | Zendy; Armin Straub | Zendy

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Special values of generalized log-sine integrals

Author(s) -

Jonathan M. Borwein,

Armin Straub

Publication year - 2011

Publication title -

nova (university of newcastle, australia)

Language(s) - English

Resource type - Conference proceedings

DOI - 10.1145/1993886.1993899

Subject(s) - sine , algebra over a field , mathematics , symbolic computation , root (linguistics) , sine qua non , pure mathematics , mathematical analysis , geometry , linguistics , philosophy

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 provided

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