The nature of g(exp(f(s))

[tommy1729]

I have to add this.

Consider h(s).

maybe h(s) behaves alot like s + 1/(exp(-s) + 1) for modest positive s.

But more interesting what if we take h(s) to behave like s + 1 + 1/f(s) !?

This gives us for some real a,b the following equation :

f( s + 1 + a/f(s) + b/f(s)^2 ) = exp(f(s)).

And maybe this f is of the type infinite composition and

f(s+1) = exp(f(s)) * t(s).

with t(s) going to 1 for large positive real part s.

This seems to make sense.

So can we find such f(s) or t(s) ??

regards

tommy1729