Picard's Little Theorem

Any entire analytic function whose range omits two points must be a constant function.

Of course, an entire function that omits a single point from its range need not be a constant, as illustrated by the function , which is entire but omits the point  from its range.

REFERENCES:

Krantz, S. G. "Picard's Little Theorem." §10.5.2 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 140, 1999.