  We investigate excitonic polaron states comprising a local exciton and
phonons in the longitudinal optical (LO) mode by solving the Schr\"{o}dinger
equation. We derive an exact expression for the ground state (GS), which
includes multi-phonon components with coefficients satisfying the Huang-Rhys
factors. The recombination of GS and excited polaron states gives one set of
sidebands in photoluminescence (PL): the multi-phonon components in the GS
produce the Stokes lines and the zero-phonon components in the excited states
produce the anti-Stokes lines. By introducing the mixing of the LO mode and
environal phonon modes, the exciton will also couple with the latter, and the
resultant polaron states result in another set of phonon sidebands. This set
has a zero-phonon line higher and wider than that of the first set due to the
tremendous number of the environal modes. The energy spacing between the
zero-phonon lines of the first and second sets is proved to be the binding
energy of the GS state. The common exciton origin of these two sets can be
further verified by a characteristic Fano lineshape induced by the coherence in
the mixing of the LO and the environal modes.
