  We present new sets of fragmentation functions for charged pions, charged
kaons, and protons, both at the leading and next-to-leading orders. They are
fitted to the scaled-momentum distributions of these hadrons measured in e+e-
annihilation on the Z-boson resonance at CERN LEP1 and SLAC SLC. These data
partly come as light-, charm-, bottom-quark-enriched and gluon-jet samples,
which allows us to treat all partons independently, after imposing the SU(2)
flavour symmetry relations. In order to gain sensitivity to the scaling
violation in fragmentation, we also include data from SLAC PEP, with
center-of-mass energy root(s)=29 GeV, in our fits. This allows us to also
determine the strong-coupling constant, with a competitive error. LEP1 data on
the longitudinal cross section as well as DESY DORIS and PETRA data at lower
energies nicely agree with theoretical predictions based on our fragmentation
functions.
