We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate ∂ F 2´x Q 2 µ ∂ ln Q 2 using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.
Analytical solutions for the non-singlet polarized parton distribution ∆q N S (x, Q 2 ) = ∆u(x, Q 2 ) − ∆d(x, Q 2 ) are obtained by solving the DGLAP equation by two analytical methods: Lagrange's Method and Method of Characteristics. The realtive merits of the two methods are discussed while comparing with HERMES data in the small x region. We also calculate the partial spin fractions carried by small x, non-singlet partons.
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