Casorati-Weierstrass Theorem

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
This example means that when n [less than or equal to] 2, the Casorati-Weierstrass theorem (i.e., f (C) is dense in C for every non-constant entire function f) is no longer true.