We review one-particle inclusive production of heavy-flavored hadrons in a framework which resums the large collinear logarithms through the evolution of the FFs and PDFs and, at the same time, retains the full dependence on the heavy-quark mass without additional theoretical assumptions. The main focus is on the production of D^* mesons in deep inelastic electron--proton scattering at HERA. We show results, neglecting for the time being the heavy-quark mass terms, for deep inelastic D^* meson production at finite transverse momenta. Work to implement this process in the above mentioned massive QCD framework is in progress.
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