スターリングの近似

ガンマ関数の漸近近似.\[\lim_{z\to\infty}\frac{\Gamma(z+1)}{\sqrt{2{\pi}z}\left(\frac{z}{e}\right)^z}=1\qquad(|\arg{z}|<{\pi})\]具体的には，\[\Gamma(z+1)\approx\sqrt{2{\pi}z}\left(\frac{z}{e}\right)^z \qquad(|\arg{z}|<{\pi},|z|\gg0)\]\[n! \approx \sqrt{2\pi n}\, \frac{n^n}{e^n}\qquad(n\gg0)\]を意味する．

Mathematics is the language with which God has written the universe.