Incomplete Gamma Functions
Let $a$ and $x$ be positive real numbers, this calculator evaluates the following five functions.
- Normalized lower incomplete gamma function $\displaystyle P(a,x)=\frac{1}{\Gamma(a)}\int_0^x t^{a-1}\mathrm{e}^{-t}\;dt$
- Normalized upper incomplete gamma function $\displaystyle Q(a,x)=\frac{1}{\Gamma(a)}\int_x^\infty t^{a-1}\mathrm{e}^{-t}\;dt$
- Non-normalized lower incomplete gamma function $\Gamma(a)P(a,x)$
- Non-normalized upper incomplete gamma function $\Gamma(a)Q(a,x)$
- Derivative of normalized lower incomplete gamma function $\displaystyle \frac{d}{dx}P(a,x)=\frac{x^{a-1}\mathrm{e}^{-x}}{\Gamma(a)}$