Asymptotics of integrals of Hermite polynomials

Richard B. Paris

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    Integrals involving products of Hermite polynomials with the weight factor exp (−x2) over the interval (−∞,∞) are considered. A result of Azor, Gillis and Victor (SIAM J. Math. Anal. 13 (1982) 879–890] is derived by analytic arguments and extended to higher order products. An asymptotic expansion in the case of a product of four Hermite polynomials Hn(x) as n→∞is obtained by a discrete analogue of Laplace’s method applied to sums.
    Original languageEnglish
    Pages (from-to)3043-3056
    Number of pages14
    JournalApplied Mathematical Sciences
    Issue number61
    Publication statusPublished - 2010


    • Moment integrals
    • Hermite polynomials
    • Asymptotic expansion


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