10/23/2016, 09:17 PM
(This post was last modified: 10/23/2016, 09:25 PM by sheldonison.)

(10/05/2016, 12:21 PM)tommy1729 Wrote: ....

So for semiexp we get the natural questions such as

The best fit ( given by the symbol = )

Mick's question on mathstack exchange is related to this post. In my answer, I considered and . See math.stackexchange.com If one uses the analytic solution for the half iterates of base_2 and the half iterate of base_e (ignoring the conjectured nowhere analytic basechange type solutions), the fractional exponentials are not at all well ordered. If a<b, half the time as x grows super exponentially large.

There are more details in my post, but if g(x)=0, then

Consider the 2nd peak for base2 occurs near 5.668, where the half iterate base_2 is larger than the half iterate base_e.

x2=sloge(sexp2(5.668 +0.5))= 5.03973936018302

xe=sloge(sexp2(5.668 ))+0.5 =5.03945210684265

The question is how much larger is x2 than xe? We can take the logarithm twice of both numbers, and compare sexp_e(x2-2) vs sexp_e(xe-2), and they differ by about +418960.3! This very large difference can be compared to the difference in log(log(2^x)) vs log(log(e^x)) which is always log(log(2)) or -0.3665

- Sheldon