The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials. (English) Zbl 1281.33006

Costas-Santos, Roberto S.; Marcellán Español, Francisco

Proc. Am. Math. Soc. 140, No. 10, 3485-3493 (2012).

The authors focus on the complementary polynomials defined by 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 R. S. Costas-Santos and 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.
With 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.

Reviewer: Teresa A. Mesquita (Vila Nova de Famalicão)

MSC:

33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C05	Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
34B24	Sturm-Liouville theory

Keywords:

classical orthogonal polynomials; Rodrigues operator; complementary polynomials; generating formula

Citations:

Zbl 1124.33011; Zbl 1204.33011

References:

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