power series for $\tanh^{-1}(z)$ I'm trying to derive the power series for $\tanh^{-1}(z)$, the inverse $\tanh$ function, and I've found that we can write $\tanh^{-1}(z)$ as $1/2\log((1+z)/(1-z))$ but I don't know how to finish off and actually find the power series.

You have the key using the logarithmic definition. Use Taylor series for Log[1+z], then for Log[1-z], substract the second from the first and divide by 2.
