- Hmmm I thought the closed form solutions are Jacobi elliptics?
- Yes. That's what the author means by
> There is a closed-form solution, but only if you extend “closed-form” to mean more than the elementary functions a student would see in a calculus class.
- My bad.
I should have encouraged more curiosity by pointing out that these functions actually have additive as well as multiplicative identities
https://msp.org/pjm/1955/5-2/pjm-v5-n2-p02-p.pdf
(Might even be relevant to the pendulum, see the comment below on the Arithmetic-Geometric Mean ;)
- Never saw that AGM expression for K0 before in the earlier linked post. Nor had I heard of the AGM, very cool.
