Gamma and beta functions (intro)
Definite integration · Mathematics
Study notes
Q: Evaluate Gamma(5) and the integral from 0 to infinity of x^4 e^(-x) dx. Gamma(1) = integral 0 to infinity of e^(-x) dx = 1. Gamma(n+1) = n Gamma(n): Gamma(2) = 1, Gamma(3) = 2, Gamma(4) = 6, Gamma(5) = 24. So the integral from 0 to infinity of x^4 e^(-x) dx = Gamma(5) = 24 = 4!.