When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?

Alfaro, Manuel; Marcellán Español, Francisco José; Peña, Ana; Rezola, M. Luisa

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When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?

Author(s): Alfaro, Manuel; Marcellán Español, Francisco José; Peña, Ana; Rezola, M. Luisa

Publisher: Elsevier

Issued date: 2010-01

Citation: Journal of Computational and Applied Mathematics, 2010, vol. 233, n. 6, p. 1446-1452

ISSN: 0377-0427

DOI: 10.1016/j.cam.2009.02.060

Sponsor: MA and MLR partially supported by Ministerio de Educación y Ciencia (MEC) of Spain under Grant MTM 2006-13000-C03-03 and Diputación General de Aragón (DGA) project E-64. FM partially supported by MEC of Spain under Grant MTM 2006-13000-C03-02 and INTAS Research Network NeCCA 03-51-6637. AP partially supported by MEC of Spain under Grants MTM 2004-03036 and MTM 2006-13000-C03-03 and DGA project E-64.

Review: PeerReviewed

Publisher version: http://dx.doi.org/10.1016/j.cam.2009.02.060

Keywords: Orthogonal polynomials , Recurrence relations , Linear functionals , Chebyshev polynomials , Difference equations

URI: http://hdl.handle.net/10016/5900

Rights: © Elsevier

Abstract:

Given {Pn}n≥0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e., [+]

Qn(x) = Pn(x) + a1Pn-1(x) + ... + akPn-k(x), ak<>0, n>k. [+]

Necessary and sufficient conditions are given for the orthogonality of the sequence {Qn}n≥0. An interesting interpretation in terms of the Jacobi matrices associated with {Pn}n≥0 and {Qn}n≥0 is shown. [+]

Description:

7 pages, no figures.-- MSC2000 codes: 33C45; 42C05.-- Issue title: "Special Functions, Information Theory, and Mathematical Physics" (Special issue dedicated to Professor Jesús Sánchez Dehesa on the occasion of his 60th birthday).

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