Definition:Gamma Function/Weierstrass Form

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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 $\C$.

Also known as

Some authors refer to the gamma function as Euler's gamma function, after Leonhard Paul Euler.

Some French sources call it the Eulerian function.

Also see

Source of Name

This entry was named for Karl Theodor Wilhelm Weierstrass.