Let $\mathbb{C}^{\mathbb{C}}$ be the D3093: Set of functions from $\mathbb{C}$ to $\mathbb{C}$.
Let $r : \mathbb{N} \to \mathbb{C}$ be a D339: Complex sequence.
The complex power series with respect to $r$ and $z_0 \in \mathbb{C}$ is the D62: Sequence \begin{equation} \mathbb{N} \to \mathbb{C}^{\mathbb{C}}, \quad N \mapsto \left( z \mapsto \sum_{n = 0}^N r_n (z - z_0)^n \right) \end{equation}

Let $\mathbb{C}^{\mathbb{C}}$ be the D3093: Set of functions from $\mathbb{C}$ to $\mathbb{C}$.
Let $r : \mathbb{N} \to \mathbb{C}$ be a D339: Complex sequence.
The complex power series with respect to $r$ and $z_0 \in \mathbb{C}$ is the D62: Sequence \begin{equation} \mathbb{N} \to \mathbb{C}^{\mathbb{C}}, \quad N \mapsto \left( f_N : \mathbb{C} \to \mathbb{C}, \quad f_N(z) = \sum_{n = 0}^N r_n (z - z_0)^n \right) \end{equation}