### Abstract

Original language | English |
---|---|

Pages (from-to) | 3043-3056 |

Number of pages | 14 |

Journal | Applied Mathematical Sciences |

Volume | 4 |

Issue number | 61 |

State | Published - 2010 |

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### Cite this

*Applied Mathematical Sciences*,

*4*(61), 3043-3056.

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*Applied Mathematical Sciences*, vol 4, no. 61, pp. 3043-3056.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotics of integrals of Hermite polynomials

AU - Paris,Richard B.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

M3 - Article

VL - 4

SP - 3043

EP - 3056

JO - Applied Mathematical Sciences

T2 - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

SN - 1312-885X

IS - 61

ER -