I am trying to compute the Complete elliptical integral of second kind kind in Mathematica with Parameter m=-19.7 .Following is the response from Mathematica.
Input:EllipticE[-19.71] Output:4.81841
I want to know if this is correct or rather how does Mathematica calculate Elliptical integrals for the parameters outside the prescribed range (-1
I am not sure I understand your question. Why do you think the output you get is wrong?
EllipticE[m] in Mathematica means the following integral -
$$ \int_0^{\pi/2} \sqrt{1-m\sin(t)}dt\,. $$
The integrand is well defined for all $ m $ and so you should expect a proper answer for all m as well. For $ m\le 1 $, this gives a real number (as you got) and for $ m > 1 $, you will get a complex number.