Tetration Forum
What am I doing wrong here? - Printable Version

+- Tetration Forum (https://math.eretrandre.org/tetrationforum)
+-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)
+--- Thread: What am I doing wrong here? (/showthread.php?tid=630)

What am I doing wrong here? - JmsNxn - 05/12/2011

I was looking at tetration and considering its little taylor series, given by:



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

RE: What am I doing wrong here? - bo198214 - 05/21/2011

(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.

RE: What am I doing wrong here? - JmsNxn - 05/26/2011

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.