The Elliptic Functions in a First-Order System

2019/03/17 by P. L. Robinson, Robinson, P. L.
Mathematics · #33E05 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:33E05

paper · pdf · doi:10.48550/arxiv.1903.07147

arxiv created 2019/03/17 · arxiv updated 2019/03/19

Abstract

We investigate the first-order system `s ' = c³, c ' = - s³; s(0) = 0, c(0) = 1'. Its solutions have the property that s c, s² and c² extend to simply-poled elliptic functions, which we explicitly identify in terms of the lemniscatic Weierstrass \wp function.

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