Hermite polynomials application for expanding functions in the series by these polynomials

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Hermite polynomials application for expanding functions in the series by these polynomials

Journal Title: Problemy Nauk Stosowanych - Year 2017, Vol 6, Issue

Abstract

Introduction and aim: Selected elementary material about Hermite polynomials have been shown in the paper. The algorithm of expanding functions in the series by Hermite polynomials has been elaborated in the paper. Material and methods: The selected knowledge about Hermite polynomials have been taken from the right literature. The analytical method has been used in this paper. Results: Has been shown the theorem describing expanding functions in a series by using Hermite polynomials. It have been shown selected examples of expanding functions in a series by applying Hermite polynomials, e.g. functions exp(az), sgn(z) and z∧2p. Conclusion: The function f(z) can be expand in the interval (-∞,+∞) in a series according to Hermite polynomials where the unknown coefficients can be determined from the orthogonality of Hermite polynomials.

Authors and Affiliations

Andrzej Antoni Czajkowski, Grzegorz Paweł Skorny, Wojciech Kazimierz Oleszak

Keywords

Hermite polynomials function of complex variable expanding functions in a series by using Hermite polynomials.

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EP ID EP219704
DOI -
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