New ₅F₄ hypergeometric transformations, three-variable Mahler measures, and formulas for 1/π

2007/04/18 by Mathew D. Rogers, Rogers, Mathew D.
Mathematics · #11F66 #33C05 #33C20 #Advanced Mathematical Identities #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT #msc:11F66 #msc:33C05 #msc:33C20

paper · pdf · doi:10.48550/arxiv.0704.2438

14 Pages

openalex publication_date 2007/04/18 · arxiv created 2008/05/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New relations are established between families of three-variable Mahler measures. Those identities are then expressed as transformations for the ₅F₄ hypergeometric function. We use these results to obtain two explicit ₅F₄ evaluations, and several new formulas for 1/π.

Related

• A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities
• Mahler measure numerology
• Transformation formulas and three-term relations for basic hypergeometric series
• Towards a change of variable formula for "hypergeometrization"
• 447 Instances of Hypergeometric 3F2(1)