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

Description of the spin structure function g_1 at arbitrary $x$ and arbitrary Q^2