# Math Help - elliptic integral

1. ## elliptic integral

Hi,

how to transform the following integral to elliptic integral of the second kind:

int 0_pi/2 (1-(k*sin(phi))^2)^-(3/2)

Thanks

2. ## Re: elliptic integral

Hi !
It's a complete elliptic integral of the third kind, in a particular case with a well-known relationship to the complete elliptic integral of the first kind.

3. ## Re: elliptic integral

Thanks JJacquelin

would you please tell me how to find the prove of the relation between the elliptic integrals of second and third kind?

4. ## Re: elliptic integral

Originally Posted by mopen80
would you please tell me how to find the prove of the relation between the elliptic integrals of second and third kind?
The relation between the elliptic integrals of second and third kind is much more complicaded (attachment)
This results from arduous work done centuries ago, when the special fuctions such as elliptic integral where in fashion.