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 |
|---|---|
| Pages (from-to) | 3043-3056 |
| Number of pages | 14 |
| Journal | Applied Mathematical Sciences |
| Volume | 4 |
| Issue number | 61 |
| Publication status | Published - 2010 |
Keywords
- Moment integrals
- Hermite polynomials
- Asymptotic expansion