03/03/2009, 06:46 PM
Are you sure that it is 1-periodic?
I mean it is well known that
\( f^{-1}(g(x))-x=\theta(x) \) must be 1-periodic
for two superexponentials f and g.
This implies that
\( g(x)=f(\theta(x)+x) \)
But
\( f(\theta(x)+x)-f(x) \) does not look 1-periodic?
\( f(\theta(x+1)+x+1)-f(x+1)=\exp(f(\theta(x)+x)))-\exp(f(x))\neq f(\theta(x)+x)-f(x) \) mostly
I mean it is well known that
\( f^{-1}(g(x))-x=\theta(x) \) must be 1-periodic
for two superexponentials f and g.
This implies that
\( g(x)=f(\theta(x)+x) \)
But
\( f(\theta(x)+x)-f(x) \) does not look 1-periodic?
\( f(\theta(x+1)+x+1)-f(x+1)=\exp(f(\theta(x)+x)))-\exp(f(x))\neq f(\theta(x)+x)-f(x) \) mostly
