### 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 language | English |
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Pages (from-to) | 3043-3056 |

Number of pages | 14 |

Journal | Applied Mathematical Sciences |

Volume | 4 |

Issue number | 61 |

Publication status | Published - 2010 |

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## Cite this

Paris, R. B. (2010). Asymptotics of integrals of Hermite polynomials.

*Applied Mathematical Sciences*,*4*(61), 3043-3056. http://www.m-hikari.com/ams/ams-2010/ams-61-64-2010/parisAMS61-64-2010.pdf