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

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(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The following relationship between $\Gamma$ and the...")
 
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<strong>[[Gamma-Sine Relation|Theorem]]:</strong> The following relationship between $\Gamma$ and the [[Sine | $\sin$]] function holds:
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<strong>[[Gamma-Sine Relation|Theorem]]:</strong> The following relationship between [[Gamma|$\Gamma$]] and the [[Sine | $\sin$]] function holds:
 
$$\Gamma(x)\Gamma(1-x) = \dfrac{\pi}{\sin(\pi x)}.$$
 
$$\Gamma(x)\Gamma(1-x) = \dfrac{\pi}{\sin(\pi x)}.$$
 
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Revision as of 04:16, 20 March 2015

Theorem: The following relationship between $\Gamma$ and the $\sin$ function holds: $$\Gamma(x)\Gamma(1-x) = \dfrac{\pi}{\sin(\pi x)}.$$

Proof: