$$ Z_j (\rho,\theta) = Z_n^m(\rho,\theta) = \begin{cases} \sqrt{2(n+1)} R_n^m(\rho) \cos m\theta, & m \ne 0, j \text{ is even} \\ \sqrt{2(n+1)} R_n^m(\rho) \sin m\theta, & m \ne 0, j \text{ is odd} \\ \sqrt{(n+1)} R_n^m(\rho), & m=0 \end{cases} $$
$$ R_n^m(\rho) = \sum_{s=0}^{(n-m)/2} \frac{(-1)^s(n-s)!}{s!\left(\frac{n+m}{2}-s\right)! \left(\frac{n-m}{2}-s\right)! } \rho^{n-2s} $$