Hi. How do I find the power series for tanh(z) (in the complex plane, if that matters, which it doesn't).

I know the power series for sinh(z) and cosh(z) (same as sin(t), cos(t), but without the sign changes):

$\displaystyle \sinh(z)=\sum_{j=0}^\infty \frac{z^{2j+1}}{2j+1!}$

$\displaystyle \cosh(z)=\sum_{j=0}^\infty \frac{z^{2j}}{2j!}$

Now what? You can't divide series (or, at a minimum, I don't know how to divide series). So what's next?

Thanks,

-J