Weierstrass-Casorati Theorem

An analytic function approaches any given value arbitrarily closely in any -neighborhood of an essential singularity.

REFERENCES:

Knopp, K. Theory of Functions Parts I and II, Two Volumes Bound as One, Part I. New York: Dover, pp. 114-115 and 124-125, 1996.

Krantz, S. G. "The Casorati-Weierstrass Theorem." §4.1.6 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 43, 1999.