• → EllipticF

EllipticE

Elliptic complete elliptic integral of the second kind (SymPy, WMA)

EllipticE[m]

computes the complete elliptic integral $E(m)$.

EllipticE[$\phi$|m]

computes the complete elliptic integral of the second kind $E(m|\phi)$.

Elliptic curves give Pi / 2 when evaluated at zero:

• • EllipticE[0]

• • EllipticE[0.3, 0.8]

Plot over a reals centered around 0:

• • Plot[EllipticE[m], {m, -2, 2}]