Searching for an asymptotic to exp[0.5]

[tommy1729]

In principle we can test how good our fake approximates the original for large x.

Lets assume our convergeance is slower then exp^[m] for positive integer m.
Fake[ exp^[m](x) ( f(x) - fake(f(x)) ] exp(- exp^[m-1](x)).

So now we can use this to get a better asymptotic.

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Another idea is to consider

F(x) = Sum a(n) x^n

A(n) = Sum b(n) x^n (1)

Now compute the fake a(n) from (1).

Call them a&(n).

Now consider fake f(x) versus Sum a&(n) x^n.

Regards

Tommy1729