The Use of Fourier Transform Methods for the Evaluation of Coefficients in a Taylor Series to Arbitrary Order.

We present a new formulation of the Taylor series for a class of functions which can be expressed as the product of a purely angular and purely radial part, viz., GR sub T Y sub lambda murfr in which Y sub lambda mu R is the spherical harmonic function. The formulation is based upon the use of the Fourier transform of the function to be expanded. The general expression for the Taylor series which we obtain is similar in form to the Laplace expansion for the Coulomb potential. Thus, Taylor series can be developed for aribtrary functions along lines which are similar to the multipolar expansions in the electromagnetic theory. Such expansions are easily adapted to the symmetry of a collection of sources. Author