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 Google™ Scholar. Others By: Area, Iván - Godoy, Eduardo - Marcellán, Francisco
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 Title: Inner products involving differences: The Meixner-Sobolev polynomials Author(s): Area, IvánGodoy, EduardoMarcellán, Francisco Publisher: Taylor & Francis Issued date: Jan-2000 Citation: Journal of Difference Equations and Applications, 2000, vol. 6, n. 1, p. 1-31 URI: http://hdl.handle.net/10016/6156 ISSN: 1023-6198 DOI: 10.1080/10236190008808211 Description: 31 pages, no figures.-- MSC2000 codes: 33C45, 33D45, 39A10, 39A70, 42C05.MR#: MR1752153 (2000m:33006)Zbl#: Zbl 0948.33004 Abstract: In this paper, polynomials which are orthogonal with respect to the inner product $$\langle p,q\rangle_S= \sum infty_{s=0} p(s)q(s) {\mu \Gamma (\gamma+s) \over\Gamma(s+1) \Gamma (\gamma)}+ \lambda \sum infty_{s=0} \Delta p(s)\Delta q(s){\mu \Gamma(\gamma+s) \over\Gamma (s+1)\Gamma (\gamma)},$$ where $0<\mu<1$, $\gamma>0$, $\lambda\ge 0$ are studied. For these polynomials, algebraic properties and difference equations are obtained as well as their relation with the Meixner polynomials. Moreover, some properties about the zeros of these polynomials are deduced. Sponsor: The work of I.A. and E.G. has been partially supported by Xunta de Galicia-Universidade de Vigo under grant 64502I703. E.G. also wishes to acknowledge partial support by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB-95-0828. The research of F.M. was partially supported by DGES of Spain under Grant PB96-1020-C03-01 and INTAS Project 93-0219 Ext. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1080/10236190008808211 Keywords: Meixner polynomialsSobolev orthogonal polynomialsDifference operatorsPollaczek polynomialsZeros of orthogonal polynomialsPolynomial approximation Rights: © Taylor & Francis Appears in Collections: DM - GAMA - Artículos de Revistas