Editing Inverse trigonometric functions (section)

====Continued fractions for arctangent====
Two alternatives to the power series for arctangent are these [[generalized continued fraction]]s:

: <math>\arctan(z) =
\frac z {1 + \cfrac{(1z)^2}{3 - 1z^2 + \cfrac{(3z)^2}{5 - 3z^2 + \cfrac{(5z)^2}{7 - 5z^2 + \cfrac{(7z)^2}{9-7z^2 + \ddots}}}}} =
\frac{z}{1 + \cfrac{(1z)^2}{3 + \cfrac{(2z)^2}{5 + \cfrac{(3z)^2}{7 + \cfrac{(4z)^2}{9 + \ddots}}}}}
</math>

The second of these is valid in the cut complex plane. There are two cuts, from &minus;'''i''' to the point at infinity, going down the imaginary axis, and from '''i''' to the point at infinity, going up the same axis. It works best for real numbers running from −1 to 1. The partial denominators are the odd natural numbers, and the partial numerators (after the first) are just (''nz'')<sup>2</sup>, with each perfect square appearing once. The first was developed by [[Leonhard Euler]]; the second by [[Carl Friedrich Gauss]] utilizing the [[Gaussian hypergeometric series]].