Carlson symmetric forms

Summary

The Carlson symmetric forms $R_F$, $R_J$, $R_C$ and $R_D$ are a standard set of elliptic integrals that are symmetric in their main arguments. Every elliptic integral can be written with them, and in particular the Legendre integrals $F$, $E$ and $\Pi$. Their symmetry gives a duplication theorem that leads to fast and stable numerical algorithms, which is why software libraries use them.