My bad.I should have encouraged more curiosity by pointing out that these functions actually have additive as well as multiplicative identities<a href="https:&#x2F;&#x2F;msp.org&#x2F;pjm&#x2F;1955&#x2F;5-2&#x2F;pjm-v5-n2-p02-p.pdf" rel="nofollow">https:&#x2F;&#x2F;msp.org&#x2F;pjm&#x2F;1955&#x2F;5-2&#x2F;pjm-v5-n2-p02-p.pdf</a>(Might even be relevant to the pendulum, see the comment below on the Arithmetic-Geometric Mean ;)

Yes. That&#x27;s what the author means by&gt; 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.

Hmmm I thought the closed form solutions are Jacobi elliptics?<a href="https:&#x2F;&#x2F;cococubed.com&#x2F;code_pages&#x2F;pendulum.shtml" rel="nofollow">https:&#x2F;&#x2F;cococubed.com&#x2F;code_pages&#x2F;pendulum.shtml</a>

Never saw that AGM expression for K0 before in the earlier linked post. Nor had I heard of the AGM, very cool.

Nonlinearity Affects a Pendulum

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