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Could be tetration if this integral converges
#33
(05/03/2014, 01:19 AM)mike3 Wrote: JmsNxn,

I am a little suspicious of this method. In particular, I'm not sure the integral

,

converges.

I totally agree. Although I added a minus sign to it, which I assume was a typo.

So lets think about .

Since the Taylor coefficients of decay EXTREMELY FAST , I consider this as a function that is well approximated by a polynomial for a long time.
( many remainder theorems for Taylor series imply this )

This means the main behaviour of this is like where n increases slowly with x.

This implies that is not bounded by a polynomial and also that = 0 infinitely often.

Therefore the integral diverges.

Even if we consider taking the limit of x going to +oo as the limit of the sequence x_i with = 0.

regards

tommy1729
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Messages In This Thread
RE: Could be tetration if this integral converges - by tommy1729 - 05/11/2014, 04:26 PM

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