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Invariant (Elliptic Function)

The invariants of a Weierstraß Elliptic Function are defined by

\begin{eqnarray*}
g_2&\equiv& 60\Sigma' {\Omega_{mn}}^{-4}\\
g_3&\equiv& 140\Sigma' {\Omega_{mn}}^{-6}.
\end{eqnarray*}



Here,

\begin{displaymath}
\Omega_{mn}\equiv 2m\omega_1-2n\omega_2,
\end{displaymath}

where $\omega_1$ and $\omega_2$ are the periods of the Elliptic Function.




© 1996-9 Eric W. Weisstein
1999-05-26