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Title: Asymptotics of integrals of Hermite polynomials
Authors: Paris, Richard B.
Affiliation: University of Abertay Dundee. School of Computing & Engineering Systems
Keywords: Hermite polynomials
Moment integrals
Asymptotic expansion
Issue Date: 2010
Publisher: Hikari Ltd
Type: Journal Article
Refereed: peer-reviewed
Rights: This is the author's final version of this article. Published version (c)Hikari Ltd., available from http://www.m-hikari.com/ams/ams-2010/ams-61-64-2010/index.html
Citation: 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
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.
URI: http://hdl.handle.net/10373/687
ISSN: 1312-885X
Appears in Collections:Computing & Engineering Systems Collection

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