Difference between revisions of "Gamma function written as infinite product"

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==Theorem==
 
==Theorem==
 
The following formula holds:
 
The following formula holds:
$$\Gamma(z) = \dfrac{1}{z} \displaystyle\prod_{k=1}^{\infty} \dfrac{(1+\frac{1}{k})^z}{1+\frac{z}{n}},$$
+
$$\Gamma(z) = \dfrac{1}{z} \displaystyle\prod_{k=1}^{\infty} \dfrac{(1+\frac{1}{k})^z}{1+\frac{z}{k}},$$
 
where $\Gamma$ denotes the [[gamma]] function.
 
where $\Gamma$ denotes the [[gamma]] function.
  

Revision as of 01:45, 1 July 2017

Theorem

The following formula holds: $$\Gamma(z) = \dfrac{1}{z} \displaystyle\prod_{k=1}^{\infty} \dfrac{(1+\frac{1}{k})^z}{1+\frac{z}{k}},$$ where $\Gamma$ denotes the gamma function.

Proof

References