Casorati-Weierstrass Theorem

a theorem in the theory of analytic functions. The theorem asserts that a single-valued analytic function in every neighborhood of an essential singularity assumes values arbitrarily close to any preassigned complex number.

The theorem was established in 1868 by Iu. V. Sokhotskii and, independently, by the Italian mathematician F. Casorati. It was published eight years later by K. Weierstrass. The theorem was first mentioned in Theory of Elliptic Functions (1859) by the French mathematicians C.-A.-A. Briot and J.-C. Bouquet. In Russian, the theorem is known as the Sokhotskii-Weierstrass theorem; in English, it is often called simply Weierstrass’ theorem.