Some remarks on exterior electromagnetic boundary value problems for spheres

An investigation of expansion problems in terms of spherical wave functions from different points of view is given. The possibility of having infinitely many formal series representations for a given function in terms of the associated Legendre functions
p_{n}^{m}
and
\sin \theta(dp_{n}^{m}/d\theta
is also pointed out. One of the representations is derived by the use of the orthogonality relation, and the infinitely many others are derived by the use of the recurrence relation.