I have a series which is expanded around $x=0$:
$$S=2 \sum_{n=0}^4 x^n (c_n\ln x+b_n)$$
where $ c_n=-\frac{1}{2}\left(\frac{(2n-1)!!}{2n!!}\right)^2$ and $b_n=-c_n\left(4 \ln 2+2\sum_{k=1}^n(\frac{1}{k}-\frac{2}{2k-1})+\frac{2}{2n-1}\right)$
I want to invert this series(i.e. x of series of function of S). How can I get this?