Searching for an asymptotic to exp[0.5]

[tommy1729]

First i considered fake function theory.
Then An elementary argument.

Those 2 led to the last 2 Posts.

However a simple argument is

S(x [1 + 1/t(x)] ) > s(x) [1 + 1/t(x)].

Omg

So simple.

Probably wrote similar stuff before , so my apologies.

However

S( x [1 + 1/u(x)] ] < s(x) [1 + 1/t(x)]

Remains An issue and the Ideas from the last few posts remain intresting.

Regards

Tommy1729