Definition:Gamma Function/Weierstrass Form

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Definition

The Weierstrass form of the Gamma function is:

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

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


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


Also see


Source of Name

This entry was named for Karl Theodor Wilhelm Weierstrass.


Sources