Some properties of the Hermite polynomials

DOI10.1515/gmj-2020-2088zbMath1494.33010OpenAlexW3122880526MaRDI QIDQ2059047

Feng Qi, Bai-Ni Guo

Publication date: 13 December 2021

Published in: Georgian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/gmj-2020-2088

zbMATH Keywords

generating functionrecurrence relationdifferential equationHermite polynomialexplicit formulaFaà di Bruno formuladerivative polynomialBell polynomials of the second kind

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Special sequences and polynomials (11B83) Other special orthogonal polynomials and functions (33C47) Elementary functions (26A09) One-variable calculus (26A06) Exponential and trigonometric functions (33B10)

Related Items (2)

Explicit, determinantal, recursive formulas and relations of the Peters polynomials and numbers ⋮ Unnamed Item

Cites Work

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• Explicit expressions for a family of the Bell polynomials and applications
• \(r\)-Bell polynomials in combinatorial Hopf algebras
• Some recurrence formulas for the Hermite polynomials and their squares
• Explicit formulas for special values of the Bell polynomials of the second kind and for the Euler numbers and polynomials
• Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations
• Explicit formulas and recurrence relations for higher order Eulerian polynomials
• Special values of the Bell polynomials of the second kind for some sequences and functions
• Some identities for a sequence of unnamed polynomials connected with the Bell polynomials
• Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind
• Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers
• The inverse of a triangular matrix and several identities of the Catalan numbers
• SEVERAL FORMULAS FOR SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND AND APPLICATIONS
• A diagonal recurrence relation for the Stirling numbers of the first kind
• Some identities related to Eulerian polynomials and involving the Stirling numbers
• Notes on two kinds of special values for the Bell polynomials of the second kind
• Diagonal recurrence relations for the Stirling numbers of the first kind

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