What is (5.3)! (i.e. 5.3 factorial)? The Gamma Function gives us a way to extend the idea of factorials to numbers that are not integers. In this video, we introduce the Gamma Function, defining it via an integral. We show that gamma(n)=(n-1)! and we compute gamma for various values, including 1/2. Along the way, we encounter the Gaussian Integral, the Euler-Mascheroni constant, the Riemann zeta function, a truly fascinating connection with the sine function, as well as volume formulas for a ball in higher dimensions (which depend on gamma).
https://youtu.be/MYM5EUBmAWA
