Working on an algebra of divergent integrals I came to the following relation: If $\tau=\int_0^\infty dx$ then $$\ln (\tau+a)=\int_0^\infty \psi'(x+1)dx-\gamma + \psi(a+1/2)$$ and this directly gives the following relation (for finite $z$): $$\frac1\pi\ln \left(\frac{\tau +\frac{z}{\pi }}{\tau...