Coloring F(x) = F(exp(x))

[tommy1729]

Post 2 is simple. G has a singularity when slog has.

The functional equations holds when g = 0.

The question is

Let ln(ln(s)) = s such that ln(s) =\= s.

What is slog(s) ? And slog(exp(s)) - slog(s) ?

Maybe naive but if n > 1 and n is the smallest n such that

Ln^[n](d_n) = d_n

Then the naive conjecture is

Slog(exp^[m](d_n)) - slog(d_n) = m mod n.

Weak version : m positive integer.
Strong version : m positive real.
Variants : negative or complex.

Regards

Tommy1729