2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132099Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and an addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.13 pages, no figuresClassical Analysis and ODEs33C45, 34B24, 35Q40, 42C05text