Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6417

 Google™ Scholar. Others By: Arvesú, Jorge - Álvarez Nodarse, Renato - Marcellán, Francisco - Kwon, Kil H.
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 Title: Some extension of the Bessel-type orthogonal polynomials Author(s): Arvesú, JorgeÁlvarez Nodarse, RenatoMarcellán, FranciscoKwon, Kil H. Publisher: Taylor & Francis Issued date: Oct-1998 Citation: Integral Transforms and Special Functions, 1998, vol. 7, n. 3-4, p. 191-214 URI: http://hdl.handle.net/10016/6417 ISSN: 1065-2469 DOI: 10.1080/10652469808819199 Description: 24 pages, no figures.-- MSC1991 codes: 33C45, 33A65, 42C05.MR#: MR1775827 (2001b:33013)Zbl#: Zbl 0936.33003 Abstract: We consider the perturbation of the classical Bessel moment functional by the addition of the linear functional $M_0\delta(x)+M_1\delta'(x)$, where $M_0$ and $M_1\in\bf R$. We give necessary and sufficient conditions in order for this functional to be a quasi-definite functional. In such a situation we analyze the corresponding sequence of monic orthogonal polynomials $B \alpha,M_0,M_1}_n(x)$. In particular, a hypergeometric representation $(_4F_2)$ for them is obtained.Furthermore, we deduce a relation between the corresponding Jacobi matrices, as well as the asymptotic behavior of the ratio $B \alpha,M_0,M_1}_n(x)/B alpha_n(x)$, outside the closed contour $\Gamma$ containing the origin, and the difference between the new polynomials and the classical ones, inside $\Gamma$. Sponsor: The work of the first three authors was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB 96-0120-C03-01. The fourth author (KHK) thanks KOSEF(95-070-02-01-3) and Korea Ministry of Education (BSR1 1420) for their research support. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1080/10652469808819199 Keywords: Bessel polynomialsSemi-classical orthogonal polynomialsHypergeometric functionsSecond order differential equationThree-term recurrence equationQuasi-orthogonal polynomialsPerturbed orthogonal polynomials Rights: © Taylor & Francis Appears in Collections: DM - GAMA - Artículos de Revistas