I have stumbled upon following transformation [imath][1 - \frac{(\pi z)^2}{6} + ...]^{-1} = [1 + \frac{(\pi z)^2}{6} + ...][/imath].
The question is simple - how was it done?
I have stumbled upon following transformation [imath][1 - \frac{(\pi z)^2}{6} + ...]^{-1} = [1 + \frac{(\pi z)^2}{6} + ...][/imath].
The question is simple - how was it done?
It is as part of the [imath]\cot(\pi z)[/imath] expansion -> [math]\cot(\pi z) = \frac{\cos(\pi z)}{\sin(\pi z)} = \frac{1}{\pi z}[1-\frac{(\pi z)^2}{2} + ...] [1 - \frac{(\pi z)^2}{6} + ...] ^{-1} = \frac{1}{\pi z} [1-\frac{(\pi z)^2}{2} + ...][1 + \frac{(\pi z)^2}{6} + ...][/math]And I don't understand the last part, where minus becomes a plus.
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