This article is cited in 2 papers

Bell polynomials in the Mathematica system and asymptotic solutions of integral equations

O. I. Marichev^a, S. Yu. Slavyanov^b, Yu. A. Brychkov<sup>c

a</sup> Wolfram Research, Champaign, IL, USA
^b Saint Petersburg State University, Petrodvorets, St. Petersburg, Russia
^c Federal Research Center "Computer Science and Control," Institution of Russian Academy of Sciences, Dorodnicyn Computing Centre of RAS, Moscow, Russia

Abstract: We consider the possibility of solving functional equations that arise when integrating homogeneous integral Fredholm equations of the second kind with a highly oscillatory kernel by using Bell polynomials. We review different types and properties of Bell polynomials. The focus of this paper is to promote using tools in the Bell polynomial package in the Mathematica system to solve certain problems in electrodynamics.

Keywords: asymptotic form of eigenfunctions of integral Fredholm equations, nonlinear functional equation, linear functional equation, saddle-point method, Kolmogorov–Arnold–Moser (KAM) theory, Bell polynomial, generalized Bell polynomial, partial Bell polynomial, Mathematica system.

Received: 05.09.2019
Revised: 09.09.2019

DOI: 10.4213/tmf9813

 English version: Theoretical and Mathematical Physics, 2019, 201:3, 1798–1807

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