QΓ函數

qΓ函數（q-Gamma function）是Γ函數的q模擬

qGamma 函數

${\displaystyle \Gamma _{q}(z)=}$${\displaystyle {\frac {(q;q)_{\infty }*(1-q)^{1-z}}{(q^{z};q)_{\infty }}}}$

其中${\displaystyle :(a;q)_{\infty }}$等符號是Q階乘冪

${\displaystyle \Gamma _{q}(1)=\Gamma _{q}(2)=1}$

${\displaystyle n!_{q}=\Gamma _{q}(n+1)}$

${\displaystyle \Gamma _{q}(z+1)={\frac {1-q^{2}}{1-q}}*\Gamma _{q}(z)}$

參考文獻

Frank Oliver,NIST Handbook of Mathematical Functions, p145, Cambridge University Press, 2010