  Orthogonal coordinate systems enable expressing the boundary conditions of
differential equations in accord with the physical boundaries of the problem.
It can significantly simplify calculations. The orthogonal similar oblate
spheroidal (SOS) coordinate system can be particularly useful for a physical
processes description inside or in the vicinity of the bodies or particles with
the geometry of an oblate spheroid. The interior solution of the Laplace
equation in the SOS coordinates was recently found; however, the exterior
solution was missing. The exterior solution of the azimuthally symmetric
Laplace equation in the SOS coordinates is derived. In the steps leading to
this solution, important formulas of the SOS algebra are found. Various forms
of the Laplace operator in the SOS coordinates in azimuthally symmetric case
are shown. General transformation between two different SOS coordinate systems
is derived. It is determined that the SOS harmonics are physically the same as
the solid harmonics. Further, a formula expressing any generalized Legendre
polynomial as a finite sum of monomials is found. The reported relations have
potential application in geophysics, astrophysics, electrostatics and solid
state physics (e.g. ferroic inclusions).
