목차

감마함수 (Gamma Function)

정의

$$ \Gamma (a) = \int_{0}^{\infty} x^{a-1} e^{-x} dx, \ a > 0 $$

특징

  1. $$ \Gamma (a) = (a-1) \Gamma (a-1) $$
  2. $a$가 정수이면, $\Gamma (a) = (a-1)!$
  3. $$ \Gamma(1) = 1 $$
  4. $$ \Gamma (1/2) = \sqrt{\pi} $$
  5. $$ \int_{0}^{\infty} x^{a-1} e^{-x/b} dx = \Gamma (a) \cdot b^{a} $$