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Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials

Published online by Cambridge University Press:  12 July 2007

José L. López  and
Nico M. Temme
José L. López
Affiliation:
Departamento de Matématica e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain ([email protected])
Nico M. Temme
Affiliation:
CWI, PO Box 94079, 1090 GB Amsterdam, The Netherlands ([email protected])
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 3 , June 2004 , pp. 537 - 555
Copyright
Copyright © Royal Society of Edinburgh 2004

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