Functional equation analogous to the 3-dimensional laplace equation

Abstract

In this thesis, we determine the general solution of a functional equation (ƒ(x + h₁,y,z) - 2ƒ(x,y,z) + ƒ(x+h₁,y,z)/h²₁) + (ƒ(x,y+h₂,z) - 2ƒ(x,y,z) + ƒ(x,y - h₂,z)/h²₂) + (ƒ(x,y,z + h₃) - 2ƒ(x,y,z) + ƒ(x,y,z - h₃)/h²₃) = 0 analogous to the 3-dimensional laplace equation [∂²/∂x² + ∂²/∂y² + ∂²/∂z²]ƒ(x,y,z) = 0.