  The explicit expressions describing the structure function g_1 at arbitrary x and Q^2 are obtained. In the first place, they combine the well-known DGLAP expressions for g_1 with the total resummation of leading logarithms of x, which makes possible to cover the kinematic region of arbitrary x and large Q^2. In order to cover the small-Q^2 region the shift Q^2 -> Q^2 + mu^2 in the large-Q^2 expressions for g_1 is suggested and values of mu are estimated. The expressions obtained do not require singular factors x^{-a} in the fits for initial parton densities. 
Description of the spin structure function g_1 at arbitrary $x$ and   arbitrary Q^2