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

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

2006-01-04

arxiv.org/abs/math/0601082v1

Mathematics

Number Theory

Scientific paper

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 Lal\'in. As a corollary, we also obtain three $q$-series expansions for the dilogarithm.

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