Generalization of the Thomson formula for homogeneous harmonic functions

Mathematical physics

In the paper, it has been shown that the Thomson formula for three-dimensional harmonic homogeneous functions in Euler terms can be generalized using a linear algebraic form involving the first order partial derivatives of the initial function instead of pure algebraic linear expressions. An exhaustive list of the formed first order expressions converting arbitrary three-dimensional harmonic functions in Euler terms into new three-dimensional homogeneous harmonic functions was presented.