The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials (Q2845865)

The authors focus on the complementary polynomials defined by \textit{H. J. Weber} in [Cent. Eur. J. Math. 5, No. 2, 415--427 (2007; Zbl 1124.33011)], here rewritten by means of the so-called Rodrigues operator introduced in a previous paper by \textit{R. S. Costas-Santos} and \textit{F. Marcellán} [Acta Appl. Math. 111, No. 1, 107--128 (2010; Zbl 1204.33011)], since a more general context is required by considering differential or difference or \(q\)-difference operators.NEWLINENEWLINENEWLINEWith respect to these complementary polynomials, this paper presents Rodrigues functional formulas, a Sturm-Liouville type equation and several informations about the corresponding generating function. In particular, this work extends the results obtained by Weber [loc. cit.] for the standard derivative operator.