Working on an algebra of divergent integrals I came to the following relation:
If $\tau=\int_0^\infty dx$ then
$$\ln (\tau+a)=\int_0^\infty \psi'(x+1)dx + \psi(a+1/2)$$
and this directly gives the following relation:
$$\frac1\pi\ln \left(\frac{\tau +\frac{z}{\pi }}{\tau -\frac{z}{\pi }}\right)...
The OP has already edited the question to remove the deprecated tag, but still, maybe somebody can suggest some further improvements - so I'll leave my comment there for a bit.
Working on an algebra of divergent integrals I came to the following relation:
If $\tau=\int_0^\infty dx$ then
$$\ln (\tau+a)=\int_0^\infty \psi'(x+1)dx + \psi(a+1/2)$$
and this directly gives the following relation:
$$\frac1\pi\ln \left(\frac{\tau +\frac{z}{\pi }}{\tau -\frac{z}{\pi }}\right)...
