Consider the following functions :
$$F(z,s)=\frac{\sin^2(\frac{c\Gamma(z)}{z})}{z^s}$$
Here, $c$ is a real constant and $s\in[0,1]$ .
Now we have to find the nature of following functional(w.r.t. given domain of $s$) :
$$\int_0^\infty\frac{F(x + iy,s) − F(x − iy,s)}{e^{2πy}-1} dy $$
as $x→∞$
Also how to analyse (for) it's zeros and local extremas (efficiently) ?