Convergent Asymptotic Expansions of Charlier, Laguerre and Jacobi Polynomials

Details Convergent Asymptotic Expansions of Charlier, Laguerre and Jacobi Polynomials Convergent Asymptotic Expansions of Charlier, Laguerre and Jacobi Polynomials

2004-10-20

arxiv.org/abs/math/0410439v1

Proc. Roy. Soc. Edinburgh Sect. A, 134A, 537--555, 2004

Mathematics

Classical Analysis and ODEs

20 pages, 5 figures. Keywords: Charlier polynomials, Laguerre polynomials, Jacobi polynomials, asymptotic expansions, saddle p

Scientific paper

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.

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