A Taylor Series in Symmetry-Adaptable Functions.

We present a Taylor series in spherical polar coordinates for a general class of functions which separate into purely angular and purely radial parts. The series depends upon the spherical harmonic functions, and, therefore, is symmetry-adaptable. The general expression for the series is developed and some specific examples are considered. In particular, we note that the Taylor series coincides with the Laplace expansion for the Coulomb potential. When the display the particular series for the exponential, exp-ar, and the inverse power law, r to the minus q power.