A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities

2006/01/04 by Mathew D. Rogers, Rogers, Mathew D. · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0601082

arxiv created 2006/01/04 · arxiv updated 2009/12/01

Abstract

We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for three-variable Mahler measures. Several of these results generalize formulas due to Condon and Lalín. As a corollary, we also obtain three q-series expansions for the dilogarithm.

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