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Chebyshevskii Sbornik, 2023, Volume 24, Issue 5, Pages 180–193
DOI: https://doi.org/10.22405/2226-8383-2023-24-5-180-193
(Mi cheb1381)
 

Some generalizations of the Faa Di Bruno formula

P. N. Sorokin

Scientific Research Institute for System Analyze of the Russian Academy of Science (Moscow)
References:
Abstract: The focus of the article is the classical Faa Di Bruno formula for computing higher-order derivatives of a complex function $F(u(x))$. Here is a version of the proof of this formula. Then we prove a generalization of the Faa Di Bruno formula to the case of a complex function with an inner function $u(x,y)$ depending on two independent variables. The paper presents a formula for the $n$-th derivative of a complex function, when the argument of the outer function is a vector with an arbitrary number of components (functions of one variable). The article also considers examples of finding higher-order derivatives, illustrating both the classical Faa Di Bruno formula and its generalizations.
Keywords: Faa Di Bruno's formula, $n$-th derivative of complex functions of several variables, generalizations of Faa Di Bruno's formula for these functions, Newton's binomial and polynomial formulas.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FNEF-2022-0007
Received: 30.08.2023
Accepted: 21.12.2023
Document Type: Article
UDC: 511.3 + 517.2
Language: Russian
Citation: P. N. Sorokin, “Some generalizations of the Faa Di Bruno formula”, Chebyshevskii Sb., 24:5 (2023), 180–193
Citation in format AMSBIB
\Bibitem{Sor23}
\by P.~N.~Sorokin
\paper Some generalizations of the Faa Di Bruno formula
\jour Chebyshevskii Sb.
\yr 2023
\vol 24
\issue 5
\pages 180--193
\mathnet{http://mi.mathnet.ru/cheb1381}
\crossref{https://doi.org/10.22405/2226-8383-2023-24-5-180-193}
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  • https://www.mathnet.ru/eng/cheb/v24/i5/p180
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