RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2019, Volume 201, Number 3, Pages 446–456 (Mi tmf9813)  

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

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).


DOI: https://doi.org/10.4213/tmf9813

Full text: PDF file (420 kB)
First page: PDF file
References: PDF file   HTML file

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

Received: 05.09.2019
Revised: 09.09.2019

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
\Bibitem{MarSlaBry19}
\by O.~I.~Marichev, S.~Yu.~Slavyanov, Yu.~A.~Brychkov
\paper Bell polynomials in the~Mathematica system and asymptotic solutions
of integral equations
\jour TMF
\yr 2019
\vol 201
\issue 3
\pages 446--456
\mathnet{http://mi.mathnet.ru/tmf9813}
\crossref{https://doi.org/10.4213/tmf9813}
\transl
\jour Theoret. and Math. Phys.
\yr 2019
\vol 201
\issue 3
\pages 1798--1807
\crossref{https://doi.org/10.1134/S0040577919120110}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077535020}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9813
  • https://doi.org/10.4213/tmf9813
  • http://mi.mathnet.ru/eng/tmf/v201/i3/p446

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:58
    References:7
    First page:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020