Computing with Harmonic Functions

Abstract: This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the Poisson integral of any polynomial can be computed exactly. This software can find exact solutions to Dirichlet, Neumann, and biDirichlet problems in R^n with polynomial data on balls, ellipsoids, and annular regions. It can also find bases for spaces of spherical harmonics, compute projections onto the harmonic Bergman space, and perform other manipulations with harmonic functions.