By expanding functions of parton fragmentation into a heavy hadron in the
inverse of the heavy quark mass mQβ we attempt to factorize them into
perturbative- and nonperturbative parts. In our approach the nonperturbative
parts can be defined as matrix elements in heavy quark effective theory, the
shape of the functions is predicted by perturbative QCD. In this work we
neglect effect at order of mQβ2β and calculate the perturbative parts at
one-loop level for heavy quark- and gluon fragmentation. We compare our results
from leading log approximation with experimental results from e+eβ
colliders and find a deviation below or at 10% level. Adding effect of higher
order in Ξ±sβ it can be expected to reduce the deviation. The size of
matrix elements appearing at the order we consider for several types of heavy
hadrons is determined.Comment: 21 pages + 3 pages figures, plain te