Abstract :
The functions of the gluon fragmentation into 3PJ quarkonium are calculated to order αs2. With the recent progress in analysing quarkonium systems in QCD we show explicitly how the so-called divergence in the limit of the zero-binding energy, which is related to P-wave quarkonia, is treated correctly in the case of fragmentation functions. The obtained fragmentation functions satisfy explicitly at the order of αs2 the Altarelli-Parisi equation and when z → 0 they behave as z−1 as expected. Some comments on the previous results are made.
