Definition:Entire Function

From ProofWiki
Jump to navigation Jump to search

Definition

Let $f: \C \to \C$ be a complex function.

Then:

$f$ is an entire function

if and only if:

$f$ is holomorphic over the whole of $\C$.


Transcendental Entire Function

Let $f$ be an entire function that has an essential singularity at $\infty$.

Then $f$ is a transcendental entire function.


Also see

  • Results about entire functions can be found here.


Historical Note

The concept of an entire function was of particular interest to Karl Weierstrass during his work on rebuilding the discipline of complex analysis.


Sources