Some extension of the Bessel-type orthogonal polynomials

We consider the perturbation of the classical Bessel moment functional by the addition of the linear functional M0 (x) + M1 0 (x), where M0 and M1 2 IR. We give necessary and su cient conditions in order for this functional to be a quasi-de nite functional. In such a situation we analyze the corresp...

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Detalles Bibliográficos
Autores: Arvesú Carballo, Jorge, Álvarez Nodarse, Renato, Marcellán Español, Francisco, Kwon, Kil Hyun
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:1998
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41730
Acceso en línea:http://hdl.handle.net/11441/41730
https://doi.org/10.1080/10652469808819199
Access Level:acceso abierto
Palabra clave:Orthogonal polynomials
Bessel polynomials
hypergeometric function
Perturbed orthogonal polynomials
Descripción
Sumario:We consider the perturbation of the classical Bessel moment functional by the addition of the linear functional M0 (x) + M1 0 (x), where M0 and M1 2 IR. We give necessary and su cient conditions in order for this functional to be a quasi-de nite functional. In such a situation we analyze the corresponding sequence of monic orthogonal polynomials B ;M0;M1 n (x). In particular, a hypergeometric representation (4F2) for them is obtained. Furthermore, we deduce a relation between the corresponding Jacobi matrices, as well as the asymptotic behavior of the ratio B ;M0 ;M1 n (x)=B n (x), outside of the closed contour containing the origin and the di erence between the new polynomials and the classical ones, inside.