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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