Let $C , D \subseteq \C$ with $z \in C \implies z + 1 \in C$.
Let $F: C \to D$ and $H: D \to D$ be holomorphic functions.
Let $H(F(z))=F(z+1)$ for all $z\in C$.
Then $F$ is said to be a superfunction of $H$, and $H$ is called a transfer function of $F$.
That is, superfunctions are iterations of transfer functions.
- This article incorporates material from Superfunction on TORI, which is licensed under the Creative Commons Attribution/Non-Commercial/Share-Alike License.