Repeated derivatives of composite functions and generalizations of the Leibniz rule

Details Repeated derivatives of composite functions and generalizations of the Leibniz rule Repeated derivatives of composite functions and generalizations of the Leibniz rule

2011-12-13

arxiv.org/abs/1112.2893v1

Mathematics

Classical Analysis and ODEs

10 pages, no figures

Scientific paper

We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of functions of the above argument, thus giving rise to expressions which can formally be interpreted as generalizations of the familiar Leibniz rule. Finally, examples of practical interest are discussed.

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