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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 201, Number 3, Pages 446–456
DOI: https://doi.org/10.4213/tmf9813 (Mi tmf9813) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

O. I. Maricheva, S. Yu. Slavyanovb, Yu. A. Brychkovc

a 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
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DOI: https://doi.org/10.4213/tmf9813
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.
Funding agency Grant number
Russian Foundation for Basic Research 17-07-00217_a
Saint Petersburg State University 40847559
The research of Yu. A. Brychkov is supported by the Russian Foundation for Basic Research (Grant No. 17-07-00217_a).
The research of S. Yu. Slavyanov is supported by St. Petersburg State University (Grant No. ID-40847559).
Received: 05.09.2019
Revised: 09.09.2019
English version:
Theoretical and Mathematical Physics, 2019, Volume 201, Issue 3, Pages 1798–1807
DOI: https://doi.org/10.1134/S0040577919120110
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: O. I. Marichev, S. Yu. Slavyanov, Yu. A. Brychkov, “Bell polynomials in the Mathematica system and asymptotic solutions of integral equations”, TMF, 201:3 (2019), 446–456; Theoret. and Math. Phys., 201:3 (2019), 1798–1807
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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