Difference between revisions of "Beta in terms of gamma"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The following formula holds: $$B(x,y)=\dfrac{\Ga...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$B(x,y)=\dfrac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)},$$ | $$B(x,y)=\dfrac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)},$$ | ||
| − | where $B$ denotes the [[beta | + | where $B$ denotes the [[beta]] function and $\Gamma$ denotes the [[gamma]] function. |
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Beta in terms of sine and cosine|next=Beta is symmetric}}: $6.2.2$ | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 15:10, 6 October 2016
Theorem
The following formula holds: $$B(x,y)=\dfrac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)},$$ where $B$ denotes the beta function and $\Gamma$ denotes the gamma function.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $6.2.2$
