** Next:** Derivation
** Up:** Normal Modes
** Previous:** Angular Modes

We now complete the formalism needed to describe the
temperature and polarization fields by adding a spatial
dependence to the modes.
By further separating the *radial* dependence
of the modes, we gain insight on their full angular structure.
This decomposition will be useful in
constructing the formal integral solutions of the perturbation
equations in §IIIC. We begin with its derivation
and then proceed to its geometric interpretation.

*Wayne Hu*

*9/9/1997*