Fundamental solutions of generalized bi-axially symmetric multivariable Helmholtz equation

TL;DR

This paper constructs explicit fundamental solutions for a generalized bi-axially symmetric multivariable Helmholtz equation and explores their properties to aid in solving boundary value problems.

Contribution

It introduces four explicit fundamental solutions for the generalized equation and analyzes their properties, advancing methods for boundary value problem solutions.

Findings

Four explicit fundamental solutions derived

Properties of solutions analyzed

Potential application to boundary value problems

Abstract

In the present article for the generalized bi-axially symmetric multivariable Helmholtz equation four fundamental solutions are constructed in explicit form. Furthermore, some properties of these solutions are shown, which will be used for solving boundary value problems for aforementioned equation.