2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110332The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions can be checked algorithmically. Hence the results can be applied in Zeilberger type algorithms for nonterminating hypergeometric series.42 pages, 2 Figures. A more compact form of hypergeometric terms is used. Examples addedClassical Analysis and ODEs33C20, 33F10text