where
are associated Legendre polynomials
and
are associated Legendre polynomials
of the second kind.
If axial symmetry then
where
are Legendre polynomials and
are Legendre polynomials of the second kind.
Match linear combinations
of the forms above
to the appropriate boundary conditions
imposed by (e.g.) conducting surfaces (equipotentials)
and any requirements that
etc.Jess H. Brewer
2005-12-24