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short compilation:fractional iteration-> eigendecomposition
For considerations of the characteristic of the powerseries of U-tetration I recently uploaded an empirical table, but this link may have been overlooked in our threads. Here it is again:
coefficients for fractional iteration
I think, I've to correct my estimation there about growth of absolute values of terms. Better estimation (instead of hypergeometric) seems to be |term_k| ~ const*exp(k^2) asymptotically by inspection of first 96 terms with fractional heights. There is a "bump" at one index k, from where the absolute values grow after they have initially decreased. This "bump" moves to higher k with |1/2-fractional(h)|-> 1/2, and maybe we can say, it moves out to infinity, if h is integer, and the beginning of growth of absolute values of terms does not occur anywhere.

An older and shorter treatize of height-dependent coefficients is in
coefficients depending on h (older) Unfortunately I choose the letter U for the matrix, which would be the matrix "POLY" in my article, so this should no more be confusing (I'll change this today or tomorrow)

Gottfried Helms, Kassel

Messages In This Thread
RE: short compilation:fractional iteration-> eigendecomposition - by Gottfried - 01/20/2008, 07:50 AM

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