Difference between revisions of "Gamma function written as infinite product"
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(Created page with "==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 ...") |
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| − | * {{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=}}: §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 09:39, 4 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
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): §1.1 (2)
