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

Research paper by Mathew D. Rogers

Indexed on: 04 Jan '06Published on: 04 Jan '06Published in: Mathematics - Number Theory

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