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

Mathew D. Rogers
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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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Mathew D. Rogers. 2006-01-04. A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities. https://arxiv.org/abs/math/0601082

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