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What are the consequences if we could express tangent via logarithm in an algebraic system? [closed]

Working on an algebra of divergent integrals I came to the following relation: If $\tau=\int_0^\infty dx$ then $$\ln (\tau+a)=\int_{0}^\infty \psi'(x+1/2+a)dx$$ and this directly gives the following ...
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