  We present two open-source (BSD) implementations of ellipsoidal harmonic
expansions for solving problems of potential theory using separation of
variables. Ellipsoidal harmonics are used surprisingly infrequently,
considering their substantial value for problems ranging in scale from
molecules to the entire solar system. In this article, we suggest two possible
reasons for the paucity relative to spherical harmonics. The first is
essentially historical---ellipsoidal harmonics developed during the late 19th
century and early 20th, when it was found that only the lowest-order harmonics
are expressible in closed form. Each higher-order term requires the solution of
an eigenvalue problem, and tedious manual computation seems to have discouraged
applications and theoretical studies. The second explanation is practical: even
with modern computers and accurate eigenvalue algorithms, expansions in
ellipsoidal harmonics are significantly more challenging to compute than those
in Cartesian or spherical coordinates. The present implementations reduce the
"barrier to entry" by providing an easy and free way for the community to begin
using ellipsoidal harmonics in actual research. We demonstrate our
implementation using the specific and physiologically crucial problem of how
charged proteins interact with their environment, and ask: what other
analytical tools await re-discovery in an era of inexpensive computation?
