A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 14th video in a series explaining the Riemann zeta function. The idea of the series is to start with basics and eventually work our way to advanced topics. The viewer is expected to understand calculus and complex numbers, whereas I will try to explain concepts from complex analysis as needed. This particular video covers the gamma function and some of its history, in preparation of getting to Riemann's functional equation next time. 00:00 - The factorial function 02:42 - The interpolation problem 04:14 - History of the interpolation problem 05:56 - How Euler's integral formula for n! works 09:45 - Visualizing Euler's integral formula 11:02 - The Gamma function 14:35 - Analytic continuation of the Gamma function 16:26 - Poles of the Gamma function 19:07 - Real plot of the Gamma function 19:59 - Complex plot of the Gamma function 20:58 - Intro to Riemann's functional equation