Next-to-leading order evolution of polarized and unpolarized fragmentation functions

We determine the two-loop ''time-like'' Altarelli-Parisi splitting functions, appearing in the next-to-leading order Q2-evolution equations for fragmentation functions, via analytic continuation of the corresponding ''space-like'' splitting functions for the evolution of parton distributions. We do this for the case of unpolarized fragmentation functions and - for the first time - also for the functions describing the fragmentation of a longitudinally polarized parton into a longitudinally polarized spin-1/2 hadron such as a Λ baryon. Our calculation is based on the method proposed and employed by Curci, Furmanski and Petronzio in the unpolarized case in which we confirm their results. (orig.)