Abstract
The spin-dependent distribution functions of the quarks and gluons inside the nucleon are investigated by solving the Altarelli-Parisi equations in the leading approximation. Using the Mellin transformations, the analytic expressions for these distribution functions are obtained. The numerical results for $0.05\ensuremath{\le}x\ensuremath{\le}0.95$ and $5 \mathrm{Ge}{\mathrm{V}}^{2}\ensuremath{\le}{Q}^{2}\ensuremath{\le}500 \mathrm{Ge}{\mathrm{V}}^{2}$ are given. The virtual-photon-nucleon spin asymmetries and the first moment of the structure function ${g}_{1}^{p}$ are also computed and compared with recent data determined from polarized deep-inelastic muon-nucleon scattering.
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