The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials

Abstract

From the Rodrigues representation of polynomial eigenfunctions of a second order linear hypergeometric-type differential (difference or q-difference) operator, complementary polynomials (see, for example, [19]) for classical orthogonal polynomials are constructed using a straightforward method. Thus a generating function in a closed form is obtained. For the complementary polynomials we present a second order linear hypergeometric-type differential (difference or q-difference) operator, a three-term recursion and Rodrigues formulas which extend the results obtained in [19] for the standard derivative operator.