Formula:KLS:01.03:04

<< Formula:KLS:01.03:03

formula in The shifted factorial and binomial coefficients

Formula:KLS:01.03:05 >>

${\displaystyle{\displaystyle{\displaystyle\binomial{\alpha}{k}:=\frac{{\left(-\alpha\right)_{k}}}{k!}(-1)^{k}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle k=0,1,2,\ldots}}}$

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
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 1.3 of KLS.

URL links

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<< Formula:KLS:01.03:03

formula in The shifted factorial and binomial coefficients

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