New $_5F_4$ hypergeometric transformations, three-variable Mahler measures, and formulas for $1/π$

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160984New relations are established between families of three-variable Mahler measures. Those identities are then expressed as transformations for the $_5F_4$ hypergeometric function. We use these results to obtain two explicit $_5F_4$ evaluations, and several new formulas for $1/π$.14 PagesNumber Theory33C20; 33C05; 11F66New $_5F_4$ hypergeometric transformations, three-variable Mahler measures, and formulas for $1/π$text