Coherent description of $D^{*\pm}$ production in $e^+e^-$ and low-$Q^2$ $e p$ collisions

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