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Define the reals $x,y$ as
$$ y = \max \Im ( W ( - exp(x)) exp(-x) ) $$
Where $W$ is the standard Lambert W function and $Im$ means the imaginary part.
How to find $x$ and $y$ ?
Closed forms ( allowing integrals , sums etc ) , contour integrals , numerical methods ??
I know how to express the...