O(ALPHA(2)(S)) CONTRIBUTIONS TO THE LONGITUDINAL FRAGMENTATION FUNCTION IN E(-) ANNIHILATION()E()

We present the order alpha(s)(2) contributions to the coefficient func tions corresponding to the longitudinal fragmentation function F-L(x, Q(2)). A comparison with the leading order alpha(s) result for F-L(x, Q(2)) shows that the corrections are large and vary from 44% to 67% in the region 0.01 < x < 0.9 at Q(2) = M(Z)(2). Our calculations also re veal that the ratio of the longitudinal and total cross section sigma( L)/sigma(tot) amounts to 0.054. This number is very close to the most recent value obtained by the OPAL collaboration which obtained 0.057 /- 0.005.