DOI: https://doi.org/10.26089/NumMet.v26r211

On the computation of higher derivatives of analytic functions

Authors

  • Anatoliy N. Gromov

Keywords:

analytic function
higher-order derivative
Cauchy integral formula
discrete Fourier transform
fast Fourier transform
interpolation Lagrange polynomial
residual term of the interpolation formula

Abstract

The representation of the derivative of an analytic function as a discrete Fourier transform with a residual term is found using the Cauchy integral formula. The estimation of the residual term is given. An example of joint use of the obtained formula and a standard computer program, in which the algorithm of fast Fourier transform is implemented, for different number of discrete samples is considered.

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Published

2025-04-22

Issue

Vol. 26 (2025): Issue 2.

Section

Methods and algorithms of computational mathematics and their applications

Author Biography

Anatoliy N. Gromov

Moscow State Institute of International Relations at Odintsovo,
Faculty of Financial Economics
• Senior Teacher

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