An analytic function approaches any given value arbitrarily closely in any 
-neighborhood of an
essential singularity.
Weierstrass-Casorati Theorem
See also
Analytic Function, Essential SingularityExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Weierstrass-Casorati TheoremCite this as:
Weisstein, Eric W. "Weierstrass-Casorati Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Weierstrass-CasoratiTheorem.html