Letting
$$K(m)=\int_0^\frac{\pi}{2}\frac{\mathrm du}{\sqrt{1-m\sin^2 u}}$$
be the Complete Integral of the First Kind, is there such an identity such that
$K(z)=K(x+iy)=f(x)+ig(y)$?
2026-03-26 09:42:24.1774518144
Splitting the Complete Elliptic Integral of the First Kind into real and imaginary functions
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