Difference between revisions of "Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0"
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==References== | ==References== | ||
| − | * {{BookReference|Higher Transcendental Functions Volume I|1953| | + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Gamma|next=Gamma function written as a limit of a factorial, exponential, and a rising factorial}}: §1.1 (1) |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 20:56, 3 March 2018
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: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): §1.1 (1)
