Common functions as CFs

$log(1+z)=\cfrac{z}{1+\cfrac{z/2}{1+\cfrac{z/6}{1+\cfrac{2z/6}{1+\cfrac{2z/10}{1+\cfrac{3z/10}{1\dots}}}}}}$

where $a_{2k}=\frac{kz}{2(2k-1)}, a_{2k+1}=\frac{kz}{2(2k+1)}$ for all $k\ges 1$ .

adamponting.com