Bessel functions of two complex mutually conjugated variables and their application in boundary-value problems of mathematical physics
We formulate boundary-value problems for the eigenvalues and eigenfunctions of the Helmholtz equation in simply connected domains by using two complex mutually conjugated variables. The systems of eigenfunctions of these problems are orthogonal in the domain. They are formed by Bessel functions of c...
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| Date: | 2017 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1703 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We formulate boundary-value problems for the eigenvalues and eigenfunctions of the Helmholtz equation in simply
connected domains by using two complex mutually conjugated variables. The systems of eigenfunctions of these problems
are orthogonal in the domain. They are formed by Bessel functions of complex variables and the powers of conformal
mappings of the analyzed domains onto a circle. The boundary-value problems for the main equations of mathematical
physics are formulated in an infinite cylinder with the use of complex and time variables. The solutions of the boundaryvalue
problems are obtained in the form of series in the systems of eigenfunctions. The Cauchy problem for the main
equations of mathematical physics with three independent variables is also considered. |
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