✦ LIBER ✦

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

✍ Scribed by Mathew D. Rogers

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 284 KB
Volume: 121
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.02.007

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✦ Synopsis

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 threevariable 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.