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
represents the Dirac delta distribution, and in addition is equal to 0 up to order m-1 at the boundary.
Boggio found that the Green's function on the ball in n spatial dimensions is The constant