# 广义组合数

$$C_{a}^{b}=\frac{a!}{b!(a-b)!}$$

$x!=\gamma(x+1)…\gamma(x)$为伽马函数

$\gamma(x)=(x-1)\gamma(x-1)$

$$C_{a}^{b}=\frac{a!}{b!(a-b)!}=\frac{\gamma (a+1)}{\gamma (b+1)\gamma(a-b+1)}$$

$$C_{4.5}^{3} =\frac{4.5!}{3!1.5!} =\frac{\gamma (5.5)}{3!\gamma (2.5)} =\frac{1}{3!}\frac{\gamma (5.5)}{\gamma(2.5)} =\frac{1}{3!}4.53.52.5$$

$$C_{3}^{4} =\frac{3!}{4!(-1)!}$$

$$C_{a}^{b}=\frac{a!}{b!(a-b)!}$$
$x!$有意义当且仅当$x\geq 0||-x\notin Z$

$$C_{3}^{4} =\frac{3!}{4!(-1)!}=\frac{1}{4}*\frac{1}{infinity}=0$$

$$C_{-1}^{3}=\frac{(-1)!}{3!*(-4)!}$$

$$C_{-1}^{-4}=\frac{(-1)!}{(-4)!*3!}$$

$$C_{x}^{n}=\frac{\prod _{i=x-n+1}^{x}i}{n!}(x\in R,n\in Z^{*})$$

$$C_{4.5}^{3}=\frac{\prod _{i=4.5-3+1}^{4.5}i}{3!}=\frac{\prod _{I=2.5}^{4.5}i}{3!}=\frac{2.53.54.5}{123}$$

$$C_{3}^{4}=\frac{\prod _{i=3-4+1}^{3}i}{4!}=\frac{\prod _{i=0}^{3}i}{4!}=\frac{0123}{1234}=0$$

$$C_{-1}^{3}=\frac{\prod _{i=-1-3+1}^{-1}i}{3!}=\frac{\prod _{i=-3}^{-1}i}{3!}=\frac{(-3)(-2)(-1)}{123}$$

…….

over

http://fightinggg.github.io/fluid/PGY13F.html

fightinggg

2018年10月21日