The distribution of zeros of general q-polynomials

A general system of q-orthogonal polynomials is de ned by means of its three-term recurrence relation. This system encompasses many of the known families of q-polynomials, among them the q-analog of the classical orthogonal polynomials. The asymptotic density of zeros of the system is shown to be a...

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Detalles Bibliográficos
Autores: Álvarez Nodarse, Renato, Buendía Ávila, Enrique, Sánchez-Dehesa Moreno-Cid, Jesús
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:1997
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41755
Acceso en línea:http://hdl.handle.net/11441/41755
https://doi.org/10.1088/0305-4470/30/19/015
Access Level:acceso abierto
Palabra clave:q-orthogonal polynomials
three-term recurrence relation
distribution of zeros
moments
Descripción
Sumario:A general system of q-orthogonal polynomials is de ned by means of its three-term recurrence relation. This system encompasses many of the known families of q-polynomials, among them the q-analog of the classical orthogonal polynomials. The asymptotic density of zeros of the system is shown to be a simple and compact expression of the parameters which characterize the asymptotic behavior of the coe cients of the recurrence relation. This result is applied to speci c classes of polynomials known by the names q-Hahn, q-Kravchuk, q-Racah,q-Askey & Wilson, Al Salam-Carlitz and the celebrated q-little and q-big Jacobi.