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.
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Acknowledgments
The authors thank N. Vasil’ev and E. Mayr for the organization of our preliminary report on the presented topic at the International Conference “Polynomial Computer Algebra 2019” (Euler International Mathematical Institute, St. Petersburg, 15–20 April 2019).
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Conflicts of interest. The authors declare no conflicts of interest.
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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).
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 201, No. 3, pp. 446–456, December, 2019.
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Marichev, O.I., Slavyanov, S.Y. & Brychkov, Y.A. Bell Polynomials in the Mathematica System and Asymptotic Solutions of Integral Equations. Theor Math Phys 201, 1798–1807 (2019). https://doi.org/10.1134/S0040577919120110
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DOI: https://doi.org/10.1134/S0040577919120110