I am looking for the Taylor series expansion of Elliptical Integral Second Kind (namely $E(\phi,k)$ and the Taylor series expansion for its inverse? Are there such expansions? (in Mathematica the name is Elliptical $E(\phi,k)$)
I will use the inverse of Elliptical $E(\phi,k)$ to approximate to a polynomial or a function. In my case phi is unknown and k is known. So an expansion approximation or polynomial approximation of the inverse is also fine that will help me to find phi.
Thanks in advance.