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We examine the parametrization of the QCD coupling in the Bethe-Salpeterequations for the hard and Regge processes and determine the argument ofalpha_s of the factorized gluon. Our analysis shows that for the hard processesalpha_s = alpha_s(k^2_T/(1- beta)) where k^2_T and beta are the longitudinaland transverse moment of the soft parton. On the other hand, in the Reggeprocesses alpha_s = alpha_s(k^2_T}/beta). We have also shown that thewell-known parametrization alpha_s = alpha_s(k^2_T) in the DGLAP equationsstands only if the lowest integration limit, mu^2, over k^2_T (the startingpoint of the Q^2 -evolution) obeys the relation mu >> Lambda_{QCD} exp{(\pi/2)}, otherwise the coupling should be replaced by the more complicatedexpression.

Parametrization of the QCD coupling in Hard and Regge processes