Some generalizations of the Faa Di Bruno formula
https://doi.org/10.22405/2226-8383-2023-24-5-180-193
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.
About the Author
Pavel Nikolaevich Sorokin
Scientific Research Institute for System Analyze of the Russian Academy of Science
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
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Review
For citations:
Sorokin P.N. Some generalizations of the Faa Di Bruno formula. Chebyshevskii Sbornik. 2023;24(5):180-193. (In Russ.) https://doi.org/10.22405/2226-8383-2023-24-5-180-193
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