Relativistic effects in the processes of heavy quark fragmentation

In the framework based on the quasipotential method and relativistic quark model a new covariant expression for the heavy quark fragmentation amplitude to fragment into the pseudoscalar and vector S-wave heavy mesons is obtained. It contains all possible relativistic corrections including the terms connected with the transformation law of the bound state wave function to the reference frame of the moving meson. Relativistic corrections of order {\bf p}^2/m^2 to the heavy quark fragmentation distributions into (\bar c c), (\bar b c) and (\bar b b) states are calculated as functions of the longitudinal momentum fraction z and the transverse momentum p_T relative to the jet axis.