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Searching for an asymptotic to exp[0.5]
(10/10/2015, 03:08 AM)sheldonison Wrote:
(10/09/2015, 11:56 AM)tommy1729 Wrote: So gaussian can not be exp ... / sqrt( 2 pi g" (h_n)).

It has to be exp( g(h_n) - n h_n) * sqrt( 2 pi g " (h_n) ).

Start with

I think your just missing a little bit of algebra. We are interested an approximation for
This is an exact equation if

see post#16 for more details on getting to this step

All of the numerical approximations I have posted, use this version of the Gaussian approximation, and get excellent results. In most cases, the Gaussian approximation is also an over-approximation of an entire function with all positive derivatives.


The reason I got confused is

1) i incorrectly thought 1/n! ~ sqrt(2 pi n) (e/n)^n.
See the fake exp.

2) I assumed the gaussian was bigger then S9 because

2 a) the Gaussian is better then S9.

2 b) You Said in post 9 that the method ( S9 ) always gives An underestimate.

So apparantly 2 b) is false.

This was not mentioned before !

Im sorry. Big misunderstanding.

Did I understand my misunderstanding Well ? Smile

Since 2 b) is false, does this imply there exist functions equal to their fake , independent of the method for fake ?
I guess so.
So we could solve S9( f(x) ) = f(x) ?


I need to read the entire thread again.




Messages In This Thread
RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/10/2015, 07:40 AM

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