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Talk: Applications and evaluations of log-sine integrals

Applications and evaluations of log-sine integrals

Date: 2011/05/19
Occasion: JonFest 2011: Workshop on Computational and Analytical Mathematics in honour of Jonathan Borwein's 60th birthday
Place: Simon Fraser University

It was my special pleasure to give this talk at JonFest 2011 in honour of Jon's 60th birthday. While the first part of the talk tries to give a nontechnical overview of our results on the evaluation of log-sine integrals, the second part shortly highlights various applications of such evaluations and connects the topic with our previous research on random walks and Mahler measures.

Abstract

Generalized log-sine integrals have appeared in recent work on the epsilon-expansion of Feynman diagrams in physics; they have also proved useful in the study of certain multiple Mahler measures. We sketch these developments and present generating functions and identies which allow for an automatic and symbolic evaluation of log-sine integrals in terms of Nielsen polylogarithms at related argument. A particular focus will be on the special arguments \(\pi/3\) and \(\pi\).

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Date: 2011/05/19
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