Log-sine evaluations of Mahler measures

2011/03/20 by Jonathan M. Borwein, Armin Straub, Borwein, Jonathan M. +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1103.3893

openalex publication_date 2011/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of multiple Mahler measures.

Citations

• Closed Forms: What They Are and Why We Care
• Log-Sine Evaluations of Mahler Measures, II

Cited by

• The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction

Related

• Log-Sine Evaluations of Mahler Measures, II
• Evaluation of iterated log-sine integrals in terms of multiple polylogarithms
• Identities between Mahler measures
• Special Values of Generalized Log-sine Integrals
• Some examples of Mahler measures as multiple polylogarithms