Entire function

In complex analysis, a function is called entire if it is defined on the whole complex plane and is holomorphic everywhere. Typical examples of entire functions are the polynomials, the exponential function, the trigonometric functions, and sums and products of those. Every holomorphic function can be represented as a power series which converges everywhere. Neither the natural logarithm nor the square root functions are entire.

The most important fact about entire functions is Liouville's theorem: an entire function which is bounded must be constant. This can be used for an elegant proof of the Fundamental Theorem of Algebra.