# Inversion of incomplete elliptic integral of the second kind

1. Jan 17, 2015

### xdrgnh

Hello I hope this is the right place to ask this question. For my thesis I need a way to invert a incomplete elliptic integral of the second kind. I believe the Jacobi elliptic functions are inverse of the elliptic integral of the first kind. The calculation I'm doing is symbolic so a numerically inverting the second integral will be no good for me. Does anyone know which function is the inverse to the elliptic integral of the second. Or perhaps I can do a coordinate transformation to turn my elliptic integral of the second kind to a elliptic integral of the first kind.

2. Jan 18, 2015

### SteamKing

Staff Emeritus
Incomplete elliptic integrals of the second kind can be expressed in terms of Jacobi elliptic functions:

http://en.wikipedia.org/wiki/Elliptic_integral#Incomplete_elliptic_integral_of_the_second_kind