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Some Properties of the Hermite Polynomials and Their Squares and Generating Functions
Version 1
: Received: 29 November 2016 / Approved: 29 November 2016 / Online: 29 November 2016 (06:50:11 CET)
A peer-reviewed article of this Preprint also exists.
Qi, F.; Guo, B.-N. Some Properties of the Hermite Polynomials. Georgian Mathematical Journal, 2021, 28, 925–935. https://doi.org/10.1515/gmj-2020-2088. Qi, F.; Guo, B.-N. Some Properties of the Hermite Polynomials. Georgian Mathematical Journal, 2021, 28, 925–935. https://doi.org/10.1515/gmj-2020-2088.
Abstract
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.
Keywords
Hermite polynomial; square; generating function; higher order derivative; differential equation; derivative polynomial; explicit formula; recurrence relation
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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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