How to Take the Factorial of Any Number

In this video, I walk through the derivation of an extension of the factorial function that works for any number: fractional, irrational, and even complex! This turns out to be a very important function, known as the gamma function, which has many surprising connections, one of which I explore in the last chapter of the video. The animations in this video were made with Manim, an open-source Python library for making math animations, originally created by 3Blue1Brown. My Previous video: Extending the Harmonic Numbers to the Reals: Chapters: 0:00 Introduction 1:38 A few Disclaimers 3:58 The Recursive Formula 6:50 The Super Recursive Formula 8:45 A minor setback 10:28 Logarithms 15:21 Deriving the Solution 19:26 Our Constraints 20:25 History and Conventions 22:16 The Miracle 25:44 The End I went for some more relaxing background music this time. Hopefully it doesn’t put y