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Consider the Mellin integral
$$K(s)=\int_{1/2}^1 \zeta\bigg(-\frac{1}{\log x}\bigg)~x^{-s}~dx $$
Where $\zeta(\cdot)$ is the Riemann zeta function defined for real $1/e<x<1.$ $K(s)$ is holomorphic on $\Bbb C$ due to the convergence on $-\infty<\Re(s)<\infty$.
We have the classical product repres...
