\begin{equation}
G^*_{lm} = N\left\{\sqrt{\left(2l+1\right)\left(2l-1\right)}R^{\alpha}_l-2\left(2l-1\right)R^{\alpha}_{l-2}\right\}Y_{l-2,m};\quad
N = \frac{1}{\sqrt{\left(2l+1\right)\left(2l-1\right)}}
\end{equation}