Inverse of Incomplete Gamma Functions 2
Let $x,p,q$ be positive real numbers and $0 < p,q < 1$, this calculator evaluates the following two functions.
- Inverse of normalized lower incomplete gamma function $P^{-1}(x,p)$, i.e. find $a=P^{-1}(x,p)$ such that $\displaystyle p=P(a,x)=\frac{1}{\Gamma(a)}\int_0^x t^{a-1}\mathrm{e}^{-t}\;dt$
- Inverse of normalized upper incomplete gamma function $Q^{-1}(x,q)$, i.e. find $a=Q^{-1}(x,q)$ such that $\displaystyle q=Q(a,x)=\frac{1}{\Gamma(a)}\int_x^\infty t^{a-1}\mathrm{e}^{-t}\;dt$