  In linear perturbation theory, all information about the growth of structure
is contained in the Green's function, or equivalently, transfer function. These
functions are generally computed using numerical codes or by phenomenological
fitting formula anchored in accurate analytic results in the limits of large
and small scale. Here we present a framework for analytically solving all
scales, in particular the intermediate scales relevant for the baryon acoustic
oscillations (BAO). We solve for the Green's function and transfer function
using spherically-averaged overdensities and the approximation that the density
of the coupled baryon-photon fluid is constant interior to the sound horizon.
