  We present new sets of fragmentation functions for D^{*+-} mesons, both at
leading and next-to-leading order. They are determined by fitting LEP1 data on
inclusive D^{*+-} production in e^+e^- annihilation. In one of the sets, we
take the charm-quark fragmentation function to be of the form proposed by
Peterson et al. and thus obtain updated values of the epsilon_c parameter and
the c -> D^{*+} branching ratio. The new fragmentation functions lead to an
excellent description of other e^+e^- data with centre-of-mass energies between
10 and 35 GeV. They also nicely agree with recent HERA data on inclusive
D^{*+-} photoproduction in ep collisions, which may be considered as a test of
the universality of the fragmentation into D^{*+-} mesons.
