} f_v^{n}(z_v&+\rho_v\xi)(f_v^{n_0})^{(t_0)}(z_v+\rho_v\xi)\cdots(f_v^{n_k})^{(t_k)}(z_v+\rho_v\xi)\notag\\ &=g_v^n(\xi)(g_v^{n_0}(\xi))^{(t_0)}\dots(g_v^{n_k}(\xi))^{(t_k)}\to g^n(\xi)(g^{n_0}(\xi))^{(t_0)}\dots(g^{n_k}(\xi))^{(t_k)}\end{aligned}$$ spherically uniformly on compact subsets of $\C.$  