Repeated derivatives of composite functions and generalizations of the Leibniz rule

DOI10.1016/j.amc.2014.04.070zbMath1334.26006arXiv1112.2893OpenAlexW1988804590WikidataQ116677413 ScholiaQ116677413MaRDI QIDQ279271

Katarzyna Górska, Giuseppe Dattoli, Karol A. Penson, Danilo Babusci

Publication date: 27 April 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.2893

zbMATH Keywords

Hermite polynomialsspecial functionsLeibniz ruleumbral methodsKampé de Fériet polynomials

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)

Related Items (3)

Quasi‐Relativistic Heat Equation via Lévy Stable Distributions: Exact Solutions ⋮ Remarks on Bell and higher order Bell polynomials and numbers ⋮ Dual numbers and operational umbral methods

Cites Work

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• The Ramanujan master theorem and its implications for special functions
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• The Hermite polynomials and the Bessel functions from a general point of view
• Exponential polynomials
• Definite integrals and operational methods
• Boson normal ordering via substitutions and Sheffer-type polynomials
• Some useful combinatorial formulas for bosonic operators
• The Curious History of Faa di Bruno's Formula
• Symbolic methods for the evaluation of sum rules of Bessel functions

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