\omega^{j + 1}
{_2F_1} \left( \left.
{
1 + j ,\
2 + j
\atop
4 + 2j
}
\right| \omega \zeta \right)
\langle h' | {^Q{\cal O}^A}_{jj} | h \rangle ,$$

To fix the diagonal part of the hard scattering amplitude we have to put ${^i\gamma^{\mit\Gamma}_j} = 0$ in Eq. (\[COPE\]), but keep the NLO result for the forward coefficient function of the polarized gluon distribution $\frac{\alpha_s}{2\pi}{^GC^A_j} (Q^2/\mu^2)$ [@PGCF; @AR88]. We can write the result as a convolution $$\begin{aligned}
\label{diagonal}
&&{^Q T_{(0)}} ( \omega, z ) \otimes F ( z, x, \zeta )
\otimes {^G {\cal O}^A} ( x, \zeta ) \\
&& \hspace{0.5cm} = - 2 \sum_{j = 0}^{\infty}
{^GC^A_j} (Q^2/\mu^2)
B( j + 1 , j + 2 ) \omega^{j + 1}
{_2F_1} \left( \left.
{
1 + j ,\
2 + j
\atop
4 + 2j
}
\right| \omega \zeta \right)
\langle h' | {^G{\cal O}^A}_{jj} | h \rangle , \nonumber\end{aligned}$$ with the following explicit expression for the function $F$, which corresponds to the DIS coefficient function in the ${\overline{\rm MS}}$ scheme [@AR88]: $$\begin{aligned}
\label{nondiagonal2}
{^GC^A}_j (Q^2/\mu^2)
&=& 2 N_f T_f \frac{6}{j}
\left\{ ( 2x - 1 )\ln \frac{Q^2\bar x}{\mu^2 x} + 3 - 4x \right\}
