  We report on the analytic calculation of the second-order QCD corrections to
semi-inclusive hadron production in electron-positron annihilation. The
calculation of the single-particle inclusive cross-section in time-like
kinematics is performed in Mellin N-space and uses an algorithmic evaluation of
inclusive phase-space integrals, based on the unitarity cutting rules and
integration-by-parts. We obtain splitting functions and coefficient functions
up to second order in the strong coupling alpha_s. Our results are in agreement
with earlier calculations in the literature by Rijken and van Neerven.
