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.
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.