 the monomial $f^n(f^{n_0})^{(t_0)}\cdots(f^{n_k})^{(t_k)}$ is replaced by the following polynomial $$\begin{aligned}  f^n(f^{n_0})^{(t_0)}\cdots(f^{n_k})^{(t_k)}+\sum_{I}c_If^{n_I}(f^{n_{0I}})^{(t_{0I})}\cdots(f^{n_{kI}})^{(t_{kI})},\end{aligned}$$ where $c_I$ is a holomorphic function on $D,$ and $n_I,n_{jI},t_{jI}$ are nonnegative integers satisfying $$\alpha_I:=\frac{ \sum_{j=0}t_{jI}}{n_I+\sum_{j=0}^kn_{jI}}<\alpha:=\frac{ \sum_{j=0}t_j}{n+\sum_{j=0}^kn_j}.$$ 