Some properties of the Hermite polynomials-Reference-Cited by-同舟云学术

Some properties of the Hermite polynomials

Published:2021-01-15 Issue:6 Volume:28 Page:925-935
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Qi Feng¹^ORCID,Guo Bai-Ni²^ORCID

Affiliation:

1. School of Mathematical Sciences , Tianjin Polytechnic University , Tianjin 300387; and College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia; and Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan , P. R. China

2. School of Mathematics and Informatics , Henan Polytechnic University , Jiaozuo , Henan, 454010 , P. R. China

Abstract

Abstract In this paper, by the Faà di Bruno formula and properties of Bell polynomials of the second kind, the authors reconsider the generating functions of Hermite polynomials and their squares, find an explicit formula for higher-order derivatives of the generating function of Hermite polynomials, and derive explicit formulas and recurrence relations for Hermite polynomials and their squares.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2020-2088/pdf

Reference24 articles.

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