The general solution to Laplace's equation in a ball centered at the origin is a linear combination of the spherical harmonic functions multiplied by the appropriate scale factor "r"ℓ,:formula_17where the formula_18 are constants and the factors formula_19 are known as solid harmonics.
The general solution to Laplace’s equation is a linear combination of the spherical harmonic functions multiplied by the solutions of "R"("r"):: formula_11where formula_12 and formula_13 are constants.