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 Google™ Scholar. Others By: Area, Iván - Godoy, Eduardo - Marcellán, Francisco - Moreno Balcázar, Juan José
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 Title: Ratio and Plancherel-Rotach asymptotics for Meixner-Sobolev orthogonal polynomials Author(s): Area, IvánGodoy, EduardoMarcellán, FranciscoMoreno Balcázar, Juan José Publisher: Elsevier Issued date: 1-Apr-2000 Citation: Journal of Computational and Applied Mathematics, 2000, vol. 116, n. 1, p. 63-75 URI: http://hdl.handle.net/10016/6140 ISSN: 0377-0427 DOI: 10.1016/S0377-0427(99)00281-2 Description: 13 pages, no figures.-- MSC codes: 42C05; 33C25; 39A10.MR#: MR1741786 (2000k:42032)Zbl#: Zbl 0984.42016 Abstract: We study the analytic properties of the monic Meixner-Sobolev polynomials $\{Q_n\}$ orthogonal with respect to the inner product involving differences $$(p,q)_S=\sum infty_{i=0}[p(i)q(i)+\lambda\Delta p(i)\Delta q(i)] {\mu (\gamma)_i\over i!},$$ $\gamma>0,\ 0<\mu<1$, where $\lambda\geq0,\ \Delta$ is the forward difference operator $(\Delta f(x)=f(x+1)-f(x))$ and $(\gamma)_n$ denotes the Pochhammer symbol. Relative asymptotics for Meixner-Sobolev polynomials with respect to Meixner polynomials is obtained. This relative asymptotics is also given for the scaled polynomials. Moreover, a zero distribution for the scaled Meixner-Sobolev polynomials and Plancherel-Rotach asymptotics for $\{Q_n\}$ are deduced. Sponsor: The work of E.G. has been partially supported by Dirección General de Enseñanza Superior (DGES) of Spain under Grant PB-96-0952. The work of F.M. is partially supported by PB96-0120-C03-01 and INTAS-93-0219 Ext. The work of J.J.M.-B. is partially supported by Junta de Andalucía, G.I. FQM0229. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1016/S0377-0427(99)00281-2 Keywords: Sobolev orthogonal polynomialsMeixner polynomialsAsymptoticsPlancherel-Rotach asymptoticsScaled polynomialsZeroes Rights: © Elsevier Appears in Collections: DM - GAMA - Artículos de Revistas