  We show the new relationship [1] between the anomalous dimensions, resummed
through next-to-next-to-leading-logarithmic order, in the
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the
first Mellin moments D{q,g}(\mu2) of the quark and gluon fragmentation
functions, which correspond to the average hadron multiplicities in jets
initiated by quarks and gluons, respectively. This relationship, which is
independent of the number of quark flavors, strongly improves previous
treatments by allowing for an exact solution of the evolution equations. So
far, such relationships have only been known from supersymmetric QCD.
