05/10/2014, 11:31 PM

(05/10/2014, 12:14 PM)sheldonison Wrote: One obvious questions from the Taylor series result, that I can't answer, because I have no idea how fast these functions grow as x goes to infinity, relative to exponentiaton. What is the "growth" of a functions like these, which should grow slower than exponentiation, but faster than any polynomial?

I mentioned these before.

They are the " fake " exp(sqrt(x)) and exp(sqrt(sqrt(x))).

since a sqrt(x) is much closer to x than any positive iterate of a logaritm it follows that they both also have growth = 1.

These sums are related to the linear ordinary differential equations.

The first is cosh(sqrt(x)).

cosh(ln(x)) < 2cosh(sqrt(x)) < cosh(x).

SO growth = 1 follows.

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Also like I said before the 0 terms do not change that much.

Maybe that makes more sense now.

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Thanks for the data !

regards

tommy1729