Notes on the Weierstrass Elliptic Function

Abstract

A consistent notation for the Weierstrass elliptic function $\wp (z;g_2,g_3)$, for $g_2>0$ and arbitrary values of $g_3$ and $\Delta \equiv g_2^3-27g_3^2$, is introduced based on the parametric solution for the motion of a particle in a cubic potential. These notes provide a roadmap for the use of {\sf Mathematica} to calculate the half-periods $({\omega }_1,{\omega }_3,{\omega }_2\equiv {\omega }_1+{\omega }_3)$ of the Weierstrass elliptic function.

9 pages, 6 figures

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