QΓ函数qΓ函数（q-Gamma function）是Γ函数的q模拟 qGamma 函数 Γ q ( z ) = {\displaystyle \Gamma _{q}(z)=} ( q ; q ) ∞ ∗ ( 1 − q ) 1 − z ( q z ; q ) ∞ {\displaystyle {\frac {(q;q)_{\infty }*(1-q)^{1-z}}{(q^{z};q)_{\infty }}}} 其中 : ( a ; q ) ∞ {\displaystyle :(a;q)_{\infty }} 等符号是Q阶乘幂 Γ q ( 1 ) = Γ q ( 2 ) = 1 {\displaystyle \Gamma _{q}(1)=\Gamma _{q}(2)=1} n ! q = Γ q ( n + 1 ) {\displaystyle n!_{q}=\Gamma _{q}(n+1)} Γ q ( z + 1 ) = 1 − q 2 1 − q ∗ Γ q ( z ) {\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
等符号是Q阶乘幂
