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

摘要

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 Lalin. As a corollary, we also obtain three q-series expansions for the dilogarithm. (C) 2006 Elsevier Inc. All rights reserved.