Difference between revisions of "Gamma function written as infinite product"
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==References== | ==References== | ||
| + | * {{BookReference|A course of modern analysis|1920|Edmund Taylor Whittaker|author2=George Neville Watson|prev=Reciprocal gamma written as an infinite product|next=}}: $\S 12 \cdot 11$ | ||
* {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Gamma function written as a limit of a factorial, exponential, and a rising factorial|next=Reciprocal gamma written as an infinite product}}: §1.1 (2) | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Gamma function written as a limit of a factorial, exponential, and a rising factorial|next=Reciprocal gamma written as an infinite product}}: §1.1 (2) | ||
Revision as of 01:37, 12 June 2016
Theorem
The following formula holds: $$\Gamma(z) = \dfrac{1}{z} \displaystyle\prod_{k=1}^{\infty} \dfrac{(1+\frac{1}{k})^z}{1+\frac{z}{n}},$$ where $\Gamma$ denotes the gamma function.
Proof
References
- 1920: Edmund Taylor Whittaker and George Neville Watson: A course of modern analysis ... (previous): $\S 12 \cdot 11$
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): §1.1 (2)
