(08/24/2010, 07:19 PM)mike3 Wrote: First off, the graph I give is not regular, it is the Cauchy-integral tetrational (which *may* be equivalent to Kneser's tetrational and the intuitive Abel-matrix one.). This tetrational is real at the real axis and decays to the conjugate fixed points toward \( \pm i \infty \). It is, however, asymptotic to regular tetrationals in the imaginary direction (but two different ones, for the two smallest-magnitude conjugate fixed points). Though your graph from the regular looks sort of like mine. (I presume you used the positive-imag-part conjugate fixed point, which would be roughly like the upper half of the Cauchy-integral tetrational.)
Hmm - what I see is, that the borders of the plot (the min-max of reals and of imags) differ obviously. Since the x0-value in the introductory msg was truncated to 12 digits the reason for the different plots *could* be such a inaccuracy. As I recalled today in the morning, that value x0 was in fact the value exp(1+0.5*i). Could you compute the min-max-limits of your graph with that exact value again? I'd like to know, whether the difference between the regular and the cauchy-integral-method is really so big.
For comparision, I have
- real_min~-42.1153427 at height h=2.54 (in new count x=1+0.5*î, h=1.54 for the old count x0=exp(1+0.5*î)),
- imag_min~ -58.97 at height h=2.68 ,
- real_max~ 60.69 at h=2.79 and
- imag_max~ 48.4 at h=2.87
(these values are all on my first picture in this thread on the magenta curve)
I'll chew the rest of your post later -
Gottfried
Gottfried Helms, Kassel
