QCD predictions for the Q$^{2}$ dependence of quark and gluon fragmentation functions using Altarelli-Parisi type equations

In the leading logarithmic approximation, the fragmentation functions of quarks and gluons are investigated using Altarelli-Parisi type equations. Using a new method to make the Mellin transformation, the equation is solved. Analytic expressions for the fragmentation functions near z=0 and z=1 are also given. Finally, numerical results for the fragmentation functions D/sub q//sup pi /, D/sub q//sup K/ are presented for different Q/sup 2/. (13 refs).