the coefficient of $x^j$ in $C_{j}^{\frac{3}{2}}
(x)$ is $3/j$ times the coefficient of $x^{j - 1}$ in $C_{j - 1}^{\frac{5}{2}} (x)$; an additional factor of 2 comes from the argument of the polynomial.

For the off-diagonal part of the amplitude we get from the conformal expansion (\[COPE\]) the following expression $$\begin{aligned}
\label{nondiagonal}
&&({\cal I} - {\cal D})
\left[
{^Q T_{(0)}} ( \omega, y ) \otimes S ( y, z )
-
{^Q T_{(0)}} ( \omega, z ) \ln ( 1 - z \omega )
\right]
\otimes
{^{QG}\!K^A} ( z, x, \zeta )
\otimes
{^G {\cal O}^A} ( x, \zeta ) \\
&& \hspace{0.5cm} = - 2 \sum_{j = 0}^{\infty}
{^{QG}\gamma^A_j}
B( j + 1 , j + 2 ) \omega^{j + 1}
\left. \frac{d}{d\rho} \right|_{\rho = 0}
{_2F_1} \left( \left.
{
1 + j + \rho,\
2 + j + \rho
\atop
4 + 2j + 2 \rho
}
\right| \omega \zeta \right)
\langle h' | {^G{\cal O}^A}_{jj} | h \rangle . \nonumber\end{aligned}$$ Its normalization is related to the LO prediction of the conformal OPE for the DVCS scattering: $${\cal F}^A_{LO} ( \omega, \zeta )
= - 2
\sum_{j = 0}^{\infty}
B( j + 1 , j + 2 )
