ellipticPi

Incomplete elliptic integral of the third kind

Approximates the integral

PI(n; phi | m) = $(INTEGRATE t=0, phi) dt/((1 - n sin²t) * sqrt( 1- m sin² t))

of amplitude phi, modulus m, and characteristic n using Gauss-Legendre quadrature.

Note that ellipticPi(PI_2, m, 1) is infinite for any m.