>> https://docs.python.org/3/library/math.html#hyperbolic-functions should be updated as well.
>
> It looks fine to me.  What do you think should be changed?

I just meant to say that the docs and the docstrings should be kept in sync (especially if they are short like in this case).  If the definition in the docs is better it could be used for the docstrings; if something gets improved in the docstring that is not already in the docs it should be added to the docs as well.  If either one is fine there's no need to update it.