On the Green function to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere

TL;DR

This paper introduces a novel method for deriving explicit Green functions for the Poisson and Helmholtz equations on the n-dimensional unit sphere, facilitating advanced solutions in mathematical physics.

Contribution

It provides a new approach to obtain closed-form Green functions for these equations on the sphere, advancing analytical techniques in this area.

Findings

Derived explicit Green functions for Poisson and Helmholtz equations

Applicable to n-dimensional spheres

Simplifies solving these equations on spherical domains

Abstract

A new method is presented to obtain a closed form of the generalized Green function to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere.