Geodesic
Bell polynomials in the~Mathematica system and asymptotic solutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 3, pp. 446-456

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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. 
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     author = {O. I. Marichev and S. Yu. Slavyanov and Yu. A. Brychkov},
     title = {Bell polynomials in {the~Mathematica} system and asymptotic solutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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O. I. Marichev; S. Yu. Slavyanov; Yu. A. Brychkov. Bell polynomials in the~Mathematica system and asymptotic solutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 3, pp. 446-456. http://geodesic.mathdoc.fr/item/TMF_2019_201_3_a10/