Some Properties of the Hermite Polynomials and Their Squares and Generating Functions

Feng Qi; Bai-Ni Guo

doi:10.20944/preprints201611.0145.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 29 November 2016 / Approved: 29 November 2016 / Online: 29 November 2016 (06:50:11 CET)

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

Hermite polynomial; square; generating function; higher order derivative; differential equation; derivative polynomial; explicit formula; recurrence relation

Computer Science and Mathematics, Analysis

Comment 1

Received: 6 December 2021
Commenter:

Feng Qi

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The commenter has declared there is no conflict of interests.

Comment: Please cite this article as

Feng Qi and Bai-Ni Guo, Some properties of the Hermite polynomials, Georgian Mathematical Journal 28 (2021), no. 6, 925--935; available online at https://doi.org/10.1515/gmj-2020-2088

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Some Properties of the Hermite Polynomials and Their Squares and Generating Functions

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