# Definition:Gamma Function/Weierstrass Form

## Definition

The Weierstrass form of the gamma function is:

$\ds \frac 1 {\map \Gamma z} = z e^{\gamma z} \prod_{n \mathop = 1}^\infty \paren {\paren {1 + \frac z n} e^{-z / n} }$

where $\gamma$ is the Euler-Mascheroni constant.

The Weierstrass form is valid for all $\C$.

## Source of Name

This entry was named for Karl Theodor Wilhelm Weierstrass.