A study of b quark fragmentation at LEP is presented using a sample of
semileptonic B decays containing a fully reconstructed charm meson, T
he data are compared to several theoretical models for heavy quark fra
gmentation; the free parameters in these models are fitted and the sen
sitivity of the model parameters to the rate of P-wave B meson product
ion is studied. The mean scaled energy fraction of B-0 and B+ mesons h
as been determined to be [x(E)] = 0.695 +/- 0.006 +/- 0.003 +/- 0.007,
where the errors are statistical, systematic and model dependence res
pectively. This result is consistent with previous, less direct measur
ements from inclusive leptonic B decays. Also presented is a model ind
ependent fit to the shape of the energy distribution of weakly decayin
g B mesons at LEP.