We analyze the second order QCD corrections to the fragmentation functions F~H_K(x, Q~2)(k = T, L, A) which are measured in e+ e- annihi- lation From these fragmentation functions one can derive the integrated transverse(σT), longitudinal(σL) and asymmetric(σ A) cross sections. The sum σ_tot =σT +σL corrected up to order a~2_s agrees with the well known result in the literature. It turns out that the order a~2_s corrections to the transverse and asymmetric quantities are small in contrast to our findings for F~H_L(x, Q~2) and σL where they turn out to be large. Therefore in the latter case one gets a better agreement between the theoretical predictions and the data obtained from he LEP experiments.
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