  We present analytic all-order results for the highest three threshold
logarithms of the space-like and time-like off-diagonal splitting functions and
the corresponding coefficient functions for inclusive deep-inelastic scattering
(DIS) and semi-inclusive e^+ e^- annihilation. All these results, obtained
through an order-by-order analysis of the structure of the corresponding
unfactorized quantities in dimensional regularization, can be expressed in
terms of the Bernoulli functions introduced by one of us and
leading-logarithmic soft-gluon exponentials. The resulting numerical
corrections are small for the splitting functions but large for the coefficient
functions. In both cases more terms in the threshold expansion need to be
determined in order to arrive at quantitatively reliable results.

High Energy Physics - Phenomenology