Notes on the Weierstrass Elliptic Function

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 $Δ\equiv g_{2}^{3} - 27 g_{3}^{2}$, 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 $(ω_{1},ω_{3},ω_{2} \equiv ω_{1} + ω_{3})$ of the Weierstrass elliptic function.

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