One of the widely used kinematic assumptions in calculating hard probe radiative energy loss within QGP, is the soft-gluon approximation, which considers that energy loss of the parent parton via gluon's bremsstrahlung is small compared to its initial energy. However, diverse theoretical formalisams obtained a notable energy loss of high $p_{\perp}$ partons, implicitly suggesting inadequacy of this approximation.

To address this issue, we relax the soft-gluon approximation within the DGLV formalism. Although the obtained analytic expressions are quite more involved compared to the soft-gluon case, the numerical predictions are surprisingly nearly indistinguishable in these two cases. Additionally, we also obtained that the above conclusion is robust with respect to variations of the presumed longitudinal distance distribution of scattering centers. Consequently, the results presented here provide confidence that, regardless of the concerns mentioned above, surprisingly, the soft-gluon approximation can reliably be applied within the DGLV formalism. Finally, we discuss generalizing the relaxation in the dynamical medium as well, which ensures broader relevance of the conclusions obtained here.