Gregory Series

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Theorem

For $-\dfrac \pi 4 \le \theta \le \dfrac \pi 4$:

$\theta = \tan \theta - \dfrac 1 3 \tan^3 \theta + \dfrac 1 5 \tan^5 \theta - \ldots$


Proof


Also see


Source of Name

This entry was named for James Gregory.


Historical Note

James Gregory established the result now known as the Gregory Series in $1671$, or perhaps earlier.