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5:40 PM
> This tag is intended for extensions of real numbers, such as hypecomplex numbers, surreal numbers, non-standard analysis, games etc.
2
Q: What are the consequences if we could express tangent via logarithm in an algebraic system?

AnixxWorking 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...

 

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