Asymptotics of integrals of Hermite polynomials
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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.
Paris, R.B. 2010. Asymptotics of integrals of Hermite polynomials. Applied Mathematical Sciences. 4(61): pp.3043-3056. Available from http://www.m-hikari.com/ams/ams-2010/ams-61-64-2010/index.html