Second structure relation for semiclassical orthogonal polynomials. (English) Zbl 1125.33008

Marcellán, Francisco; Sfaxi, Ridha

J. Comput. Appl. Math. 200, No. 2, 537-554 (2007).

Authors’ summary: Classical orthogonal polynomials are characterized from their orthogonality and by a first or second structure relation. For the semiclassical orthogonal polynomials (a generalization of the classical ones), the authors find only the first structure relation in the literature. In this paper, they establish a second structure relation. In particular, they deduce it by means of a general finite-type relation between a semiclassical polynomial sequence and the sequence of its monic derivatives.

Reviewer: Francisco Perez Acosta (La Laguna)

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

Keywords:

finite-type relation; recurrence relations; orthogonal polynomials; semiclassical linear functionals

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