Difference between revisions of "Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0"
From specialfunctionswiki
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==References== | ==References== | ||
* {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Gamma|next=Gamma function written as a limit of a factorial, exponential, and a rising factorial}}: §1.1 (1) | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Gamma|next=Gamma function written as a limit of a factorial, exponential, and a rising factorial}}: §1.1 (1) | ||
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 07:21, 16 June 2016
Theorem
The following formula holds: $$\Gamma(z) = \displaystyle\int_0^1 \log \left( \dfrac{1}{t} \right)^{z-1} \mathrm{d}t,$$ where $\Gamma$ denotes the gamma function and $\log$ denotes the logarithm.
Proof
References
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): §1.1 (1)
