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ON THE STUDY OF VARIOUS REPRESENTATIONS OF SOLUTIONS OF QUASI-DIFFERENTIAL EQUATIONS IN THE FORM OF SUMS OF SERIES AND THEIR SOME APPLICATIONS
- Authors: Vatolkin M.Y.1
-
Affiliations:
- M.T. Kalashnikov Izhevsk State Technical University
- Issue: Vol 64, No 11 (2024)
- Pages: 2058-2076
- Section: Ordinary differential equations
- URL: https://ogarev-online.ru/0044-4669/article/view/277200
- DOI: https://doi.org/10.31857/S0044466924110041
- EDN: https://elibrary.ru/KGSNLM
- ID: 277200
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Abstract
In the theory of the matrix equation _𝑋 = 𝐴(𝑡)𝑋, the well-known representation of the solution in the form of a series plays an important role. In the case of an 𝑛-th order scalar equation, it is also interesting to get a representation of the solution in the form of a scalar series, the terms of which are constructed from the coefficients of the original equation. Various representations of the fundamental system of solutions of a homogeneous quasi-differential equation of the 𝑛-th order in the form of scalar series, the terms of which are constructed from the coefficients of the original equation, are studied. As an example, in the form of such series, representations of the elements of the fundamental system of solutions of the Bessel equation are constructed, considered in the interval [#,+∞), where # > 0.
About the authors
M. Yu. Vatolkin
M.T. Kalashnikov Izhevsk State Technical University
Email: vmyu6886@gmail.com
Izhevsk, Russia
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