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.

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