Difference between revisions of "Gamma(z)Gamma(1-z)=pi/sin(pi z)"

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==Theorem==
<strong>[[Gamma-Sine Relation|Theorem]]:</strong> The following relationship between $\Gamma$ and the [[Sine | $\sin$]] function holds:
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The following formula holds:
$$\Gamma(x)\Gamma(1-x) = \dfrac{\pi}{\sin(\pi x)}.$$
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$$\Gamma(z)\Gamma(1-z) = \dfrac{\pi}{\sin(\pi z)},$$
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where $\Gamma$ denotes the [[gamma]] function and $\sin$ denotes the [[sine]] function.
<strong>Proof:</strong> █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[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.

Proof

References