12/20/2009, 08:01 AM
(12/20/2009, 06:31 AM)Ansus Wrote: It is possible to use this formula and substitute sexp as inverse function operator of slog.
\( \operatorname{slog}_z C=-\int \left( \frac{1}{z (\ln z)^2}\sum_{q=0}^{\operatorname{slog}_z C -1}\frac{1}{D_q \operatorname{sexp}_z(q-1)}\right) dz \)
Then it will be an iterating formula for slog.
But this approach is complicated.
Why would it be so complicated? If we represent our slog as a powerseries, we can apply the Lagrange inversion theorem. Also, what should be the bounds on the integral? And if this is too complicated, is there anything simpler?
