The Heavy Quark Fragmentation Function at NNLO

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We present a general discussion of collider processes with not-completely inclusive production of heavy flavors. We review the Perturbative Fragmentation Functions formalism as the appropriate tool for studying such processes and detail the extension of this formalism at Next-to-Next-to-Leading order. We conclude that the prospects for the future in this field are bright and at present are limited by the available experimental data. Hopefully, the future ILC will be able to fill this gap.