# Definition:Superfunction

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## Definition

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 $\map H {\map F z} = \map F {z + 1}$ 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.

## Also see

## Sources

*This article incorporates material from Superfunction on TORI, which is licensed under the Creative Commons Attribution/Non-Commercial/Share-Alike License.*

*WARNING: This link is broken. The TORI site seems to no longer exist.*