05/12/2015, 09:55 PM

First i want to say that the equation

Slog(ln(x)) = slog(x) - 1 is sometimes better then

Slog(exp(x)) = slog(x) + 1.

Basically because slog is NOT periodic as the exp suggests.

Also because we almost always only consider the fixpoint x = ln(x) rather then all the fixpoints x = exp(x).

Let the fixpoints be L and L*.

First question

Im fascinated by the fact that f(g(x)+1) can be periodic while g is not.

Are there elementary nonpolynomial f,g that satisfy this ?

Second question

How does slog behave around the singularities at L and L* ??

3rd question

Does there exist An entire function E such that,

Slog(x) = E( ln(x - L) + ln(x - L*) ) ?

Or something similar ?

Regards

tommy1729

Slog(ln(x)) = slog(x) - 1 is sometimes better then

Slog(exp(x)) = slog(x) + 1.

Basically because slog is NOT periodic as the exp suggests.

Also because we almost always only consider the fixpoint x = ln(x) rather then all the fixpoints x = exp(x).

Let the fixpoints be L and L*.

First question

Im fascinated by the fact that f(g(x)+1) can be periodic while g is not.

Are there elementary nonpolynomial f,g that satisfy this ?

Second question

How does slog behave around the singularities at L and L* ??

3rd question

Does there exist An entire function E such that,

Slog(x) = E( ln(x - L) + ln(x - L*) ) ?

Or something similar ?

Regards

tommy1729