Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials
Fecha
2004Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
|
10.1017/S0308210500003334
Resumen
Convergent expansions are derived for three types of orthogonal polynomials:
Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large
values of the degree. The expansions are given in terms of functions that are special
cases of the given polynomials. The method is based on expanding integrals in one or
two points of the complex plane, these points being saddle points of ...
[++]
Convergent expansions are derived for three types of orthogonal polynomials:
Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large
values of the degree. The expansions are given in terms of functions that are special
cases of the given polynomials. The method is based on expanding integrals in one or
two points of the complex plane, these points being saddle points of the phase
functions of the integrands. [--]
Materias
Charlier polynomials,
Laguerre polynomials,
Jacobi polynomials,
Convergent expansions
Editor
Cambridge University Press
Publicado en
Proceedings of the Royal Society of Edinburgh, 134A, 537–555, 2004
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Versión del editor
Entidades Financiadoras
J.L.L. thanks the CWI of Amsterdam for its scientific and financial support
during the realization of this work. The financial support of the savings bank, Caja
Rural de Navarra, is also acknowledged.