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What am I doing wrong here?
#1
I was looking at tetration and considering its little taylor series, given by:
(1)

where:

and:



specifically, what I was trying to do is find a relationship between the coefficients of tetrations' little taylor series and normal taylor series. We'll say:


so I'm looking for as an expression of or vice versa.

So I started off by looking at (1):







and now let this equal our formula for sexp(x+1) using or the normal taylor series.



and subtract the right hand side from the left hand side



and now, since x is essentially arbitrary, let x = l to give:


but this contradicts the original Taylor series expansion


which states:


Any help would be greatly appreciated, thanks.

The only solution I have is
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#2
(05/12/2011, 07:53 PM)JmsNxn Wrote:

One problem could be that if you let x=l then . And calculating with infinities is always somewhat risky.
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#3
oh, that's obvious there in the first equation. I hate missing stuff that's right in front of me.

yeah, I've really started to notice that infinity is difficult to work with. It frustrated me at first but then I realize it comes with the territory.
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