Re: Tetration again!

Am 23.12.2007 20:57 schrieb mike3:
On Dec 23, 5:22 am, Gottfried Helms <he...@xxxxxxxxxxxxx> wrote:
Am 23.12.2007 09:48 schrieb mike3:

Hmm. However I still don't seem to get how to compute
the polynomials. Is there an "easy" (simple) algorithm for
the coefficients of the powers of h in those polynomials?
Hmm, if you're able to find an easier, for instance recurrence,
formula - this would be a big shot, I'd guess...


Well, maybe then there wasn't an "easy" algorithm, but how does
one do the "hard" algorithm? How do you use that matrix to get
the polynomials? I didn't seem to see anything in the link you
posted that showed explicitly how to derive the polynomials from
that matrix.
How to get a polynomial from consecutive values?
find a polynomial in h for [f(0),f(1),f(2),...] = [1,1,1,1,1,1,...]
This is constant so f(h) = 1

find a polynomial in h for [f(0),f(1),f(2),...] = [0,1,2,3,4,5,6,...]
Compute differences delta1 = [1,1,1,1,1,1,...] - this is constant,
so the polynomial has order 1.

find a polynomial in h for [f(0),f(1),f(2),...] = [0,0,1,3,6,10,15,...]
Compute differences delta1 = [0,1,2,3,4,5,...] -
Compute differences delta2 = [1,1,1,1,1,1,...] -
this is constant,
so the polynomial has order 2.

How actually the polynomials are built by hand, you may find at
wikipedia or mathworld... if I recall right, in wikipedia the
explanation was very elementar and instructive.

Gottfried


--
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Gottfried Helms, Kassel
.

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