  The complete soft-enhanced and virtual-gluon contributions are derived for
the quark coefficient functions in semi-inclusive e^+e^- annihilation to the
third order in massless perturbative QCD. These terms enable us to extend the
soft-gluon resummation for the fragmentation functions by two orders to the
next-to-next-to-next-to-leading logarithmic (N^3LL) accuracy. The resummation
exponent is found to be the same as for the structure functions in inclusive
deep-inelastic scattering. This finding, together with known results on the
higher-order quark form factor, facilitates the determination of all soft and
virtual contributions of the fourth-order difference of the coefficient
functions for these two processes. Unlike the previous (N^2LL) order in the
exponentiation, the numerical effect of the N^3LL contributions turns out to be
negligible at LEP energies.
