ON THE HERMITE POLYNOMIALS AND THEIR SERIES CONVERGENCE

Authors

Wagner Alfredo Moreira Mera Instituto de Posgrado Universidad Técnica de Manabí, Portoviejo, Ecuador. https://orcid.org/0009-0001-3394-6703
Adrián Ramón Infante Línares Department of Mathematics, Universidad Simón Bolívar, A.P. 89000 Caracas, Venezuela https://orcid.org/0000-0003-2451-8413

DOI:

https://doi.org/10.33936/revbasdelaciencia.v7iESPECIAL.4791

Keywords:

Hermite Polynomials, Complex Hermite Polynomial, convergence in series.

Abstract

In this paper we make a study of the results on the properties of the Hermite polynomials. These polynomials form a family of orthogonal polynomials with respect to the Gaussian measure and it is a closed system. We present the basic properties until we introduce the convergence of Fourier-Hermite series. We also present a definition for Hermite polynomials with a certain parameter, as an extension of these polynomials in the classical form, motivating to study complex Hermite poly- nomials and their properties.

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