  Recursive solution for a general homogeneous in time pure birth branching
process with simultaneous production of any number of particles and with
continuous evolution parameter is given. Calculational algorithm based on the
use of Koenigs function and functional Schroder equation is described. It is
shown that multiplicity distributions in e+e- annihilation into hadrons for
c.m. energies up to 189 GeV are well described by the modified negative
binomial distribution, explained by simple pure birth branching process without
multiple simultaneous particle production. The energy dependence of the
evolution parameter is also discussed.
