GeoDom: New Regularization Method for Divergent Series
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For $x \in (-1, 1)$, the series $\sum_{n=0}^{\infty} e^{-i (2n + 1) \cos^{-1}(x)}$ is divergent, but we can obtain regularized results using
Both $(*)$ and $(**)$ allow for a slight generalization, since $(1-2)$ from the aforementioned link are generalized in the formula $(22)$ of the same link.
Which gives a Grandi-type series. Therefore, the approach above provides another very elementary way to account for $-i + i - i + i - i + i \dots = -\frac{i}{2}$.
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