Upper approximation of $\mathrm{atanh}(x)$? Is there are nice upper approximation of $\mathrm{atanh(x)}$?
For example, $\ln(x)$ is nicely approximated by $x-1$ for $x$ around $1$.

$$Atanh(x) = \sum_{k=0}^{\infty} \frac{x^{1+2 k}}{1+2 k}, |x|<1$$
And
$$Atanh(x) = -\frac{\pi \sqrt{-x^2}}{2 x}+\sum_{k=0}^{\infty} \frac {x^{-1-2 k}}{1+2 k}, |x|>1$$
You can approximate it by using $$\sum_{k=0}^n$$ and decide what $n$ gives the level of approximation you need.
