A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities
arXiv:math/0601082
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 -series expansions for the dilogarithm.