Particular solutions of the multidimensional singular ultrahyperbolic equation generalizing the telegraph and Helmholtz equations

Authors

  • Z.O. Arzikulov Fergana State Technical University, Fergana, Uzbekistan; National Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”, Tashkent, Uzbekistan https://orcid.org/0009-0004-2965-4566
  • T.G. Ergashev National Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”, Tashkent, Uzbekistan https://orcid.org/0000-0003-3542-8309

DOI:

https://doi.org/10.31489/2025m2/16-27

Keywords:

particular solution, Lauricella function, multiple confluent hypergeometric function, a limit correlation theorem, a system of the partial differential equations

Abstract

This article deals with the construction of particular solutions for a second-order multidimensional singular partial differential equation, which generalizes the famous telegraph and Helmholtz equations. The constructed particular solutions are expressed in terms of the multiple confluent hypergeometric function, which is analogous to the multiple Lauricella function and the famous Bessel function. A limit correlation theorem for the multiple confluent hypergeometric function is proved, and a system of partial differential equations associated with the confluent function is derived. Thanks to the proven properties of the multiple confluent hypergeometric function. The particular solutions of the multidimensional partial differential equation with the singular coefficients are written in explicit forms and it is determined that these solutions have a singularity at the vertex of a multidimensional cone.

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Published

2025-06-30

How to Cite

Arzikulov, Z., & Ergashev, T. (2025). Particular solutions of the multidimensional singular ultrahyperbolic equation generalizing the telegraph and Helmholtz equations. Bulletin of the Karaganda University. Mathematics Series, 118(2), 16–27. https://doi.org/10.31489/2025m2/16-27

Issue

Section

MATHEMATICS