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We derive the Leading-Order(LO) master equation to
extract the polarized gluon distribution $ G(x,Q^2)=x \delta
g(x,Q^2)$ from polarized proton structure function,
$g^{p}_{1}(x,Q^{2})$. By using a Laplace-transform technique, we
solve the master equation and derive the polarized gluon
distribution inside the proton. The test of accuracy which is
based in our calculations on two different methods, confirms
that we achieve to the correct solution for the polarized gluon
distribution. To determine the polarized gluon distribution $x \delta g(x,Q^2)$ more accuratly , we only need to have more experimental data on the polarized structure functions,
$g_1^{p}(x,Q^2)$. Our result for polarized gluon distribution is in good agreement with some phenomenological models.
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