  Calculations of one-electron spectral functions, optical conductivity and
spin-wave energy in the Holstein double-exchange model are made using the
many-body coherent potential approximation. Satisfactory agreement is obtained
with angle-resolved photoemission results on La_1.2Sr_1.8Mn_2O_7 and optical
measurements on Nd_0.7Sr_0.3MnO_3. A pseudogap in the one-electron spectrum at
the Fermi level plays an important role in both systems, but a small-polaron
band is only predicted to exist in the La system. A rigorous upper bound on
spin-wave energies at T=0 is derived. The spin-wave stiffness constant D
decreases with increasing electron-phonon coupling g in a similar way to the
Curie temperature Tc, but D/(k_B Tc) increases for large g (low Tc) as observed
experimentally.
