Fundamental Solution of Dirichlet Boundary Value Problem of Axisymmetric Helmholtz Equation

Abstract

Fundamental solution of Dirichlet boundary value problem of axisymmetric Helmholtz equation is constructed via modified Bessel function of the second kind, which unified the formulas of fundamental solution of Helmholtz equation, elliptic type Euler-Poisson-Darboux equation and Laplace equation in any dimensional space.