In the mathematical field of potential theory, Boggio's formula is an explicit formula for the Green's function for the polyharmonic Dirichlet problem on the ball of radius 1. It was discovered by the Italian mathematician Tommaso Boggio.
The polyharmonic problem is to find a function u satisfying
where m is a positive integer, and
where
Boggio found that the Green's function on the ball in n spatial dimensions is
The constant