Parametrization of the QCD coupling in the evolution equations

We examine the parametrization of the QCD coupling in the evolution equations, including DGLAP. Our conclusion is that the well-known parametrization, where the argument of the coupling is k⊥2/β or just k⊥2, stands only if the lowest integration limit in the transverse momentum space (the starting point μ2 of the Q2-evolution) obeys the relation μ≫ΛQCDexp(π/2), otherwise the coupling should be replaced by the more complicated expression presented in Eq. (29).