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\[∑n =\infty \tan -1 (2n)\]

Did I do it correctly?

Learning this in the beginning myself

This is an infinite sum

Whoops, I meant
\[\int_{\color{red}1}^\infty\arctan\frac{1}{x^2}\,dx\]

nice problem

I think this does rest of the job
http://www.math.umn.edu/~garrett/m/complex/hadamard_products.pdf