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Searching for an asymptotic to exp[0.5]
About issues 2) and 3) and in general ...

Suppose we want the correcting factors c_n for f(x).

Since a_n depends on the truncated fake Taylor polynomial of degree n ,
At best we can take ^(2/n) < as explained before >.

But there is another upperbound.

F(x)^q needs to satisfy the fundamental conditions

D^a [F(x)^q] > 0 for a E (0,1,2).

In particular a = 2.

This places An upper bound on q INDEP of n but DEP on the values and rate of descent of the a_n.

And this is the balance we look for

:

the faster a_n descends , the larger q is.
And vice versa.

There we cannot " repeat the argument " as much as we want , nor choose any m-th root we want ( or other function ).

This gives hope for proving results of type

Correcting factors ~< O ( ( ln(n) n)^gamma ).

gamma ~ 1/2 is then close to a proof of TPID 17.

I call Q = 1/q the power level of f(x).

Guess this clarifies alot.

Im not sure how this relates to sheldon's integrals , Hadamard products and zeration [ min,- algebra ] yet.
Although I have Some Ideas ...

Regards

Tommy1729
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RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/05/2015, 08:16 AM

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