Methods and algorithms of computational mathematics and their applications

On the computation of higher derivatives of analytic functions

A. N. Gromov

Moscow State Institute of International Relations

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.

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

UDC: 519.6

Received: 04.03.2025
Accepted: 01.04.2025

DOI: 10.26089/NumMet.v26r211