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A germ at a point is an equivalence class of functions defined on a neighbourhood of the point: two representatives are equivalent if they agree on some smaller neighbourhood. A germ of a holomorphic function requires its representatives to be holomorphic functions; smooth and continuous germs use their corresponding classes of functions. The germ retains local behavior while forgetting the representative's values farther from the point.

A germ at $z\in D$ is an equivalence class $[f{]}_z$ of holomorphic functions defined near $z$, where two representatives are equivalent when they agree on some neighbourhood of $z$.

It is the holomorphic-function case of a germ.