The Elliptic Functions in a First-Order System

P. L. Robinson

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arXiv · 1903.07147

The Elliptic Functions in a First-Order System

P. L. Robinson

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Abstract

We investigate the first-order system `$s\,' = c^3, \, c\,' = - s^3; \, s(0) = 0, \, c(0) = 1$'. Its solutions have the property that $s \, c$, $s^2$ and $c^2$ extend to simply-poled elliptic functions, which we explicitly identify in terms of the lemniscatic Weierstrass $\wp$ function.

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P. L. Robinson. 2019-03-17. The Elliptic Functions in a First-Order System. https://arxiv.org/abs/1903.07147

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