  Starting 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.
