Hi all, glad to present the first try to the inverse elliptic integral of the second kind. Please try it yourself and give us a feedback!

% modulus and phase in degrees

[phi,alpha] = meshgrid(0:5:90, 0:2:90);

% values of integrals

[F,E] = elliptic12(pi/180*phi, sin(pi/180*alpha).^2);

% values of inverse

invE = inverselliptic2(E, sin(pi/180*alpha).^2);

Refs:

% modulus and phase in degrees

[phi,alpha] = meshgrid(0:5:90, 0:2:90);

% values of integrals

[F,E] = elliptic12(pi/180*phi, sin(pi/180*alpha).^2);

% values of inverse

invE = inverselliptic2(E, sin(pi/180*alpha).^2);

Refs:

- http://code.google.com/p/elliptic/source/browse/trunk/inverselliptic2.m
- J. P. Boyd, "Numerical, Perturbative and Chebyshev Inversion of the Incomplete Elliptic Integral of the Second Kind", Applied Mathematics and Computation (January 2012)