Higher Order Heavy Quark Corrections to Deep-Inelastic Scattering

The 3-loop heavy flavor corrections to deep-inelastic scattering are essential for consistent next-to-next-to-leading order QCD analyses. We report on the present status of the calculation of these corrections at large virtualities Q2. We also describe a series of mathematical, computer-algebraic and combinatorial methods and special function spaces, needed to perform these calculations. Finally, we briefly discuss the status of measuring αs(MZ), the charm quark mass mc, and the parton distribution functions at next-to-next-to-leading order from the world precision data on deep-inelastic scattering.