A harmonic polynomial is a polynomial 
on 
that is a harmonic function,
so it satisfies Laplace's equation
 |
Every homogeneous polynomial 
of total degree 
has a unique decomposition
 |
where 
denotes the floor function, 
is the Euclidean norm,
and each 
is zero or a harmonic homogeneous polynomial
of total degree 
. Restricting these harmonic homogeneous
polynomials to the unit sphere gives the spherical
harmonics.
