Formula:KLS:01.09:01

<< The q-shifted factorial

formula in The q-gamma function and q-binomial coefficients

Formula:KLS:01.09:02 >>

${\displaystyle{\displaystyle{\displaystyle{}\Gamma_{q}\left(x\right):=\frac{\left(q;q\right)_{\infty}}{\left(q^{x};q\right)_{\infty}}(1-q)^{1-x}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle 0<q<1}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Gamma_{q}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-gamma function : http://dlmf.nist.gov/5.18#E4
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 1.9 of KLS.

URL links

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<< The q-shifted factorial

formula in The q-gamma function and q-binomial coefficients

Formula:KLS:01.09:02 >>