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1. ERROR ESTIMATES FOR DOMINICI'S HERMITE FUNCTION ASYMPTOTIC FORMULA AND SOME APPLICATIONS.

Author

Kerman, R., Huang, M. L., and Brannan, M.

Subjects
*HERMITE polynomials, *MATHEMATICAL formulas, *GREEN functors, *FOURIER transforms, *DIGITAL filters (Mathematics), *PROBABILITY theory, *DIFFERENTIAL equations, *DIFFERENTIAL operators, *HYPERGEOMETRIC functions, *BESSEL functions, *PROOF theory
Abstract

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. [ABSTRACT FROM AUTHOR]

Published
2009
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