2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215876We characterize, up to a conjecture, probability distributions of all order finite moments having ultraspherical type generating functions for orthogonal polynomials.Some proofs are shortened. There is an insight into the stated conjectureProbabilityClassical Analysis and ODEs42C05; 33C05; 33C45text