The Abel equation for the slog was .

Our original recurring for the super exponential (which I will call similarly) sexp is .

So if we develop it at 0, say satisfying the inverted Abel equation:

we get

where is the complete Bell polynomial.

The left side develops to and so we have the infinite equation system

And I wonder if we solve it the natural way whether we get exactly the inverse of the slog (which I assume). Unfortunately there is no complete Bell polynomial in Maple (at least I didnt find it) and I am too lazy in the moment to program it myself

And yes, it is not a linear equation system. Perhaps it is despite solvable, who knows ...

Our original recurring for the super exponential (which I will call similarly) sexp is .

So if we develop it at 0, say satisfying the inverted Abel equation:

we get

where is the complete Bell polynomial.

The left side develops to and so we have the infinite equation system

And I wonder if we solve it the natural way whether we get exactly the inverse of the slog (which I assume). Unfortunately there is no complete Bell polynomial in Maple (at least I didnt find it) and I am too lazy in the moment to program it myself

And yes, it is not a linear equation system. Perhaps it is despite solvable, who knows ...