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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Modelling, Analysis and Simulation [MAS]
Computational Dynamics

López, J.L, & Temme, N.M. (2003). Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials. Modelling, Analysis and Simulation [MAS]. CWI.