Difference between revisions of "Gamma(z)Gamma(1-z)=pi/sin(pi z)"
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m (Tom moved page Gamma-Sine Relation to Euler's reflection formula for gamma) |
m (Tom moved page Euler's reflection formula for gamma to Gamma(z)Gamma(1-z)=pi/sin(pi z)) |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
| − | $$\Gamma( | + | $$\Gamma(z)\Gamma(1-z) = \dfrac{\pi}{\sin(\pi z)},$$ |
| − | + | where $\Gamma$ denotes the [[gamma]] function and $\sin$ denotes the [[sine]] function. | |
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| + | ==References== | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 11:54, 5 April 2018
Theorem
The following formula holds: $$\Gamma(z)\Gamma(1-z) = \dfrac{\pi}{\sin(\pi z)},$$ where $\Gamma$ denotes the gamma function and $\sin$ denotes the sine function.
