Formula:KLS:01.03:03

<< Formula:KLS:01.03:02

formula in The shifted factorial and binomial coefficients

Formula:KLS:01.03:04 >>

${\displaystyle{\displaystyle{\displaystyle{}\binomial{\alpha}{\beta}:=\frac{\Gamma\left(\alpha+1\right)}{\Gamma\left(\beta+1\right)\Gamma\left(\alpha-\beta+1\right)}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1

Bibliography

Equation in Section 1.3 of KLS.

URL links

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<< Formula:KLS:01.03:02

formula in The shifted factorial and binomial coefficients

Formula:KLS:01.03:04 >>