Expansion of a function about a displaced center

Abstract

A simpler, more general version of a formula given by Sharma for the expansion of functions of the form, $F\left(\overrightarrow{\mathrm{r}}\right)=f\left(r\right)\mathrm{}{Y}_l^m(\theta , \phi )$, in terms of spherical harmonics and radial functions at a new origin, is derived from an earlier treatment of the expansion problem based on Fourier transforms.