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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 e^z, which is entire but omits the point z=0 from its range.


See also

Entire Function, Picard's Great Theorem

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References

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

Referenced on Wolfram|Alpha

Picard's Little Theorem

Cite this as:

Weisstein, Eric W. "Picard's Little Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PicardsLittleTheorem.html

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