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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.
Georgian Mathematical Journal – de 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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