real slog developed at a fixed point

[bo198214]

.. So for example:
\( r_1=\frac{\lambda_1}{1-\eta_1}=\frac{1/2}{1-\el} \)
\( r_2=... \)

Could you type your expression for the
\( r_0 \)?

Well \( r_0 \) has to be chosen such that \( \text{slog}(0)=-1 \), i.e
\( -1=\text{slog}(0)=\frac{1}{\el}\left(\log(-\el) + r_0+\sum_{n=1}^\infty r_n (-\el)^n\right) \)
i.e.
\( r_0=-\el-\log(-\el)-\sum_{n=1}^\infty r_n (-\el)^n \)
*headscratch, is that correct?*