A general asymptotic expansion formula for integrals involving high-order orthogonal polynomials

Emmanuel Perrey-Debain, I. David Abrahams

    Research output: Contribution to journalArticlepeer-review

    Abstract

    A new method of evaluating overlap integrals involving orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. For a large class of polynomials and for sufficiently large orders, these coefficients can be written explicitly as Taylor series in terms of powers of ε = 1/n, where n is the polynomial order. Such decompositions are perfectly suited to the accurate numerical evaluation of integrals involving high-order polynomials. Examples include the numerical evaluation of integrals involving classical orthogonal polynomials such as Laguerre, Jacobi, and Gegenbauer. © 2009 Society for Industrial and Applied Mathematics.
    Original languageEnglish
    Pages (from-to)3884-3904
    Number of pages20
    JournalSIAM Journal on Scientific Computing
    Volume31
    Issue number5
    DOIs
    Publication statusPublished - 2009

    Keywords

    • Asymptotic expansion of integrals
    • Orthogonal polynomial
    • Quasi-classical approximation
    • Transition matrix

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