A lesson on generating functions, and clever uses of complex numbers for counting Help fund future projects: An equally valuable form of support is to simply share the videos. Special thanks: #thanks Artwork by Kurt Burns Music by Vince Rubinetti Nice writeup and video giving solutions to the exercises at the end, by Benjamin Hackl 102 Combinatorial problems, by Titu Andreescu and Zuming Feng Generatingfunctionology by Herbert Wilf Visualizing the Riemann zeta function Fourier series Timestamps 0:00 - Puzzle statement and motivation 4:31 - Simpler example 6:51 - The generating function 11:52 - Evaluation tricks 17:24 - Roots of unity 26:31 - Recap and final trick 30:13 - Takeaways Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ These animations are largely made using a custom python library, manim. See the FAQ comments here: #manim You can find code for specific videos and projects here: Music by Vincent Rubinetti. Download the music on Bandcamp: Stream the music on Spotify: ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: Various social media stuffs: Website: Twitter: Reddit: Instagram: Patreon: Facebook: