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Some properties of the Hermite polynomials

Some properties of the Hermite polynomials AbstractIn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Some properties of the Hermite polynomials

Georgian Mathematical Journal , Volume 28 (6): 11 – Dec 1, 2021

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Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2020-2088
Publisher site
See Article on Publisher Site

Abstract

AbstractIn 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.

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2021

Keywords: Hermite polynomial; generating function; differential equation; derivative polynomial; explicit formula; recurrence relation; Faà di Bruno formula; Bell polynomials of the second kind; 33C45; 11B83; 26A06; 26A09; 26A24; 33B10; 33C47; 34A05

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