Mathematical Facts

Table of Contents

• Contents
  • Analysis

Contents

Analysis

• If $X \sim N(0, \sigma^2)$, then $\mathbb{E}[X^{2n}] = \sigma^{2n} (2n - 1)!!.$
• (Stirling’s Formula) $n! \sim \sqrt{2\pi n} \left(\frac{n}{e}\right)^n.$
• (Wallis Product) $\frac{\pi}{2} = \prod_{n=1}^{\infty} \frac{4n^2}{4n^2 - 1}.$