Asymptotics of integrals of Hermite polynomials

Richard B. Paris

Research output: Contribution to journalArticle

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Abstract

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
Volume4
Issue number61
StatePublished - 2010

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Hermite polynomials
Polynomials
Product integral
Laplace
Asymptotic expansion
Higher order
Analogue
Interval

Cite this

Paris, Richard B. / Asymptotics of integrals of Hermite polynomials.

In: Applied Mathematical Sciences, Vol. 4, No. 61, 2010, p. 3043-3056.

Research output: Contribution to journalArticle

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Asymptotics of integrals of Hermite polynomials. / Paris, Richard B.

In: Applied Mathematical Sciences, Vol. 4, No. 61, 2010, p. 3043-3056.

Research output: Contribution to journalArticle

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