A lesson on generating functions, and clever uses of complex numbers for counting
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Artwork by Kurt Burns
Music by Vince Rubinetti

Nice writeup and video giving solutions to the exercises at the end, by Benjamin Hackl
https://benjaminhackl.at/blog/2022/0...
   • Solutions to 3b1b's generating functi...  

102 Combinatorial problems, by Titu Andreescu and Zuming Feng
https://amzn.to/3wAPoNq

Generatingfunctionology by Herbert Wilf
https://amzn.to/3sPJ8Al

Visualizing the Riemann zeta function
   • But what is the Riemann zeta function...  

Fourier series
   • But what is a Fourier series?  From h...  

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:
https://www.3blue1brown.com/faq#manim'>https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/

You can find code for specific videos and projects here:
https://github.com/3b1b/videos/

Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/

Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/a...

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...



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