廿TT

譬如水怙牛過窓櫺 頭角四蹄都過了 因甚麼尾巴過不得

メモ:第二種不完全ガンマ関数の積分

\displaystyle \int^{\infty}_{y} \Gamma(k,x) \, dx = \frac{e^{-y}y^{k+1}+(k-y) \Gamma(k+1,y)}{k}


f:id:abrahamcow:20150827030049p:plain
Wolfram|Alpha: Computational Knowledge Engine

#Rで確かめ算
> Igamma <- function(a,x){
+ pgamma(x, a, lower=FALSE) * gamma(a)
+ }
> integrate(function(x)Igamma(2,x),3,Inf)
0.2489353 with absolute error < 9.3e-05
> IIgamma <-function(y,k){
+ (exp(-y)*y^(k+1)+(k-y)*Igamma(k+1,y))/k
+ }
> IIgamma(3,2)
[1] 0.2489353