〈 Berger | Dillon 〉

Cool! I tried proving it myself, then found a proof online and it's much more complicated than I expected. So, it's kind of obvious that this will converge exponentially, but it's fun to see: by the fourth term, the relative error from 1/24 is about 10⁻¹⁰

Can you link to the proof you found? Though I can see that there’s a potential link to a sum of residues that @ValFadeev identifies, I can’t figure out a contour that actually exploits this.