Formula di Stirling

Related

• Limiti
• Calcolo Differenziale (class)

Formula

$$\underset{n\to +\infty }{\lim }\frac{n!}{n^n\cdot e^{-n}\cdot \sqrt{2\pi n}}=1$$ $$n!\backsimeq n^n\cdot e^{-n}\cdot \sqrt{2\pi n}$$

Osservazione

$$\underset{n\to \infty }{\lim }\frac{x^n\cdot n!}{n^n}=\{\begin{array}{ll}+\infty & \text{se }x\ge e\\ 0& \text{se }x<e\end{array}$$