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.
|Number of pages||14|
|Journal||Applied Mathematical Sciences|
|Publication status||Published - 2010|