  A high order series expansion is employed to study the thermodynamical
properties of a S=1/2 chain coupled to dispersionless phonons. The results are
obtained without truncating the phonon subspace since the series expansion is
performed formally in the overall exchange coupling J. The results are used to
investigate various parameter regimes, e.g. the adiabatic and antiadiabatic
limit as well as the intermediate regime which is difficult to investigate by
other methods. We find that dynamic phonon effects become manifest when more
than one thermodynamic quantity is analyzed.
