The Elliptic Functions in a First-Order System

Abstract

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

Cited by in corpus (2)

• Meromorphic functions in a first-order system
• Higher Trigonometry: A Class Of Nonlinear Systems