QΓ函数

qΓ函数（q-Gamma function）是Γ函数的q模拟

qGamma 函数

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

其中${\displaystyle :(a;q)_{\infty }}$等符号是Q阶乘幂

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

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

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

参考文献

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