Analysis of Low-$x$ Gluon Density from the $F_2$ Scaling Violations

We present an analysis of the current methods of approximate determination of the gluon density $G(x,Q^2)$ at low-$x$ from the scaling violations of the proton structure function $F_2(x,Q^2)$. The gluon density is obtained from DGLAP equation by expansion at distinct points of expansion. We show that the different results given by the proposed methods can be obtained from one new expression considering the adequate points of expansion. It is shown in which case the approximate determination of $G(x,Q^2)$ is reasonable.