Searching for an asymptotic to exp[0.5]

[tommy1729]

I noticed Q9 must give about the same result as S9 for the exp(x) in the sense that

There exists fixed positive real constants A,B such that

A < S9(n)/Q9(n) < B

for all positive integer n.

[ S9(n) is the sheldon post 9 estimate of a_n and Q9(n) is my Q9 estimate of a_n ]

Therefore it seems intuitive to conjecture

The SQ conjecture :

A < S9(n)/Q9(n) < B

where the fixed positive real values A,B only depend on the function considered.

***


I wonder what S9 and Q9 give for the J(x) function.
( the J(x) function that estimates the binary partition function discussed before ... J for Jay D fox )

If there exists a counterexample to the SQ conjecture that is entire , then it probably has to do alot with convergeance speed.

regards

tommy1729