So I tried to take the inverse of EllipticE when modulus is large, in Mathematica, but the solution gives wrong answer.
InverseSeries[Series[EllipticE[x, -k], {x, 0, 12}, {k, Infinity, 1}],y] = InverseFunction[y,k]
For example, I tried EllipticE[0.5,-9.9] = 0.656
where x:0.5 , k:-9.9, y:0.656
But InverseFunction[y,k] is not equal to 0.5. Am I not correctly taking the inverse of the function?
I need a general form of an equation for the inverse of EllipticE. Polynomial approximation is also fine. The approximation should definitely work around when x-->0
and k-->-infinity
.
So for the above example, the approximation function result should yield to 0.5 when y=0.656 and k=-9.9. I need to code this function in MCU, so I need an analytical approximation.
Caner