A New Generating Function for Hermite Polynomials

This paper presents a new generating function of the form gx,t=∑n=0∞tnHnex for Hermite polynomials and reveals its connection with the incomplete gamma function. Recurrence relations of Hermite polynomials and another version of its contour integral representation are derived from this version of th...

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Main Author: Manouchehr Amiri
Format: Article
Language:English
Published: Wiley 2025-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/ijmm/9075713
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author Manouchehr Amiri
author_facet Manouchehr Amiri
author_sort Manouchehr Amiri
collection DOAJ
description This paper presents a new generating function of the form gx,t=∑n=0∞tnHnex for Hermite polynomials and reveals its connection with the incomplete gamma function. Recurrence relations of Hermite polynomials and another version of its contour integral representation are derived from this version of the generating function. New versions of the generating functions for the two-variable Hermite polynomials have been presented.
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spelling doaj-art-83c13a7adf4e4fab84947b6fbb63d5e62025-08-20T03:12:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252025-01-01202510.1155/ijmm/9075713A New Generating Function for Hermite PolynomialsManouchehr Amiri0Independent ResearcherThis paper presents a new generating function of the form gx,t=∑n=0∞tnHnex for Hermite polynomials and reveals its connection with the incomplete gamma function. Recurrence relations of Hermite polynomials and another version of its contour integral representation are derived from this version of the generating function. New versions of the generating functions for the two-variable Hermite polynomials have been presented.http://dx.doi.org/10.1155/ijmm/9075713
spellingShingle Manouchehr Amiri
A New Generating Function for Hermite Polynomials
International Journal of Mathematics and Mathematical Sciences
title A New Generating Function for Hermite Polynomials
title_full A New Generating Function for Hermite Polynomials
title_fullStr A New Generating Function for Hermite Polynomials
title_full_unstemmed A New Generating Function for Hermite Polynomials
title_short A New Generating Function for Hermite Polynomials
title_sort new generating function for hermite polynomials
url http://dx.doi.org/10.1155/ijmm/9075713
work_keys_str_mv AT manouchehramiri anewgeneratingfunctionforhermitepolynomials
AT manouchehramiri newgeneratingfunctionforhermitepolynomials