Riemann- zeta function (III)

Calculus Level 5

True or false? \[\displaystyle \frac{-1}{2} \left (\pi z \cot (\pi z) - 1 \right) = \sum_{n = 1}^{\infty} \zeta (2n) z^{2n}\] in \(D(0, 1) \subset \mathbb{C}\), after eliminating the avoidable singularity of \(\pi z \cot (\pi z)\) at \(z = 0\).

Note.-

a) \(\zeta ( \cdot )\) is Riemann zeta function.

b) we are assuming Axiom of Choice according to main principles of "constructive mathematics".

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