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