10/08/2015, 08:41 AM
(10/08/2015, 03:41 AM)sheldonison Wrote: \( f(x)=\exp\( (\ln(x))^2 \) \;\;\; g(x) = \ln (f(\exp(x))) \)
\( g(x)=x^2 \;\;\; g'(x)=2x \;\;\; g''(x)=2 \;\;\; h_n=\frac{n}{2} \)
\( a_n \approx \frac{\exp(g(h_n) - n h_n)}{\sqrt{2 \pi g''(h_n) }} \;\;\; \approx \frac{ \exp(-\frac{n^2}{4}) }{ \sqrt{4 \pi} } \)
Yes but this exp ( - n^2 / 4 ) is far from Jay's 2 ^ ( - n (n-1) ) / n !
Its a different base ; exp(- 1/4) =\= 2^(-1).
So this is the worst fit , rather then the best ?
It seems to disprove the conjectures ?!
Or do i need less or more medication ?
Regards
Tommy1729
