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 Google™ Scholar. Others By: García-Caballero, Esther M. - Moreno, Samuel G. - Marcellán, Francisco
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 Title: Generating functions and companion symmetric linear functionals Author(s): García-Caballero, Esther M.Moreno, Samuel G.Marcellán, Francisco Publisher: Akadémiai Kiadó Issued date: Jun-2003 Citation: Periodica Mathematica Hungarica, 2003, vol. 46, n. 2, p. 157-170 URI: http://hdl.handle.net/10016/5989 ISSN: 0031-5303 (Print)1588-2829 (Online) DOI: 10.1023/A:1025988010220 Description: 14 pages, no figures.-- MSC2000 codes: 33C45, 42C05.MR#: MR2004670 (2004i:33016)Zbl#: Zbl 1047.33004 Abstract: In this contribution we analyze the generating functions for polynomials orthogonal with respect to a symmetric linear functional u, i.e., a linear application in the linear space of polynomials with complex coefficients such that $$u\left({x 2n+1}}\right)=0$$. In some cases we can deduce explicitly the expression for the generating function $${\mathcal{P}}\left({x,w}\right)=\sum\limits_{n=0} infty {c_n P_n \left(x \right)w ,}$$ where {Pn}n is the sequence of orthogonal polynomials with respect to u. Sponsor: Second author (S.G.M.)'s research supported by Junta de Andalucía, Grupo de Investigación FQM 0178. Third author (F.M.)'s research supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain, Grant BFM 2000-0206-C04-01 and INTAS Project 2000-272. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1023/A:1025988010220 Keywords: Orthogonal polynomialsGenerating functionsSymmetric linear functionals Rights: © Springer Appears in Collections: DM - GAMA - Artículos de Revistas