Error estimates for Dominici's Hermite function asymptotic formula and some applications

Ron Kerman, Mei Ling Huang, Michael Brannan


The aim of this paper is to find a concrete bound for the error involved when approximating the nth Hermite function (in the oscillating range) by an asymptotic formula due to D. Dominici. This bound is then used to study the accuracy of certain approximations to Hermite expansions and to Fourier transforms. A way of estimating an unknown probability density is proposed.



Hermite function; asymptotic formula; Green’s function; Hermite expansion; Fourier transform; density estimation


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.