Appel polynomials associated with Fourier transforms and their applications to differential equations
https://doi.org/10.22405/2226-8383-2024-25-3-213-225
Abstract
Formulas for the coefficients of the expansion into a series of Appel polynomials associated with a differential equation of parabolic type are obtained. It has been established that Appel polynomials are involved in the formulas for the expansion of the solution to the Cauchy problem for equations of parabolic type into a series of derivatives of the fundamental solution.
A new method for solving the Cauchy problem is proposed, the essence of which is to use series
expansion in Appel polynomials. The results generalize the method for solving the heat equation
on the real axis by expanding it into a series of Hermite polynomials. The connection between
the Fourier transform and series in associated Appel polynomials is studied. The issue of using Hermite polynomials for the Laplace transform has been studied.
About the Authors
Alexander Ivanovich Nizhnikov
Moscow State Pedagogical University
Russian Federation
Russian Federation
Oleg Emmanuilovich Yaremko
Moscow State Technical University “Stankin”
Russian Federation
Russian Federation
Natalya Nikolaevna Yaremko
National Research Technological University “MISiS” (Moscow).
Russian Federation
Russian Federation
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Review
For citations:
Nizhnikov A.I., Yaremko O.E., Yaremko N.N. Appel polynomials associated with Fourier transforms and their applications to differential equations. Chebyshevskii Sbornik. 2024;25(3):213-225. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-3-213-225
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