Definition:Gamma Function/Weierstrass Form

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Definition

The Weierstrass form of the Gamma function is:

$\displaystyle \frac 1 {\Gamma \left({z}\right)} = z e^{\gamma z} \prod_{n \mathop = 1}^\infty \left({\left({1 + \frac z n}\right) e^{-z / n} }\right)$

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