




The integrand in the integral formula for arctan, , can be expanded in a geometric series, which can be integrated term by term to get a series formula for arctan y:
Integrating term by term we get
(Integrating term by term is ok if the resulting series is absolutely convergent, which this series is when y < 1.)
We can use this series to obtain a formula for .
The tangent of which means that :
This gives us