Casorati–Weierstrass theorem

In complex analysis, a branch of mathematics, the Casorati–Weierstrass theorem describes the behaviour of holomorphic functions near their essential singularities. It is named for Karl Theodor Wilhelm Weierstrass and Felice Casorati. In Russian literature it is called Sokhotski's theorem.

Start with some open subset U in the complex plane containing the number ${\displaystyle z_{0}}$, and a function f that is holomorphic on ${\displaystyle U\ \backslash \ \{z_{0}\}}$, but has an essential singularity at ${\displaystyle z_{0}}$ . The Casorati–Weierstrass theorem then states that

...
Wikipedia