2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160739We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.13 pages, 1 figureComplex Variables30F45; 33C05; 33C75; 33E05text