05/26/2008, 10:56 AM
Hi everybody !
Concerning:
I tried to figure, via Mathematica, the Henryk's plots and the results are shown in the "Sqrtwobase" attachment. As far as the x^x plot, for x < 0, I propose the second attachment, also obtained by Mathematica ("Totalxtox").
The first file suggests a conjecture. The second file is selfexplanatory (I hope).
I am happy to discuss with you again.
Gianfranco
Concerning:
andydude Wrote:... , I wondered whether or not those discontinuities (in the graphs) were necessary, but ... it seems that there is no way to remove them with analytic continuation, maybe I'm wrong.
Also, another nice plot is the Re/Im parametric plot of this same data. I used to compare that to the parametric plot of Re/Im of \( x^x \) as x goes from zero to negative infinity, but I never found anything...
I tried to figure, via Mathematica, the Henryk's plots and the results are shown in the "Sqrtwobase" attachment. As far as the x^x plot, for x < 0, I propose the second attachment, also obtained by Mathematica ("Totalxtox").
The first file suggests a conjecture. The second file is selfexplanatory (I hope).
I am happy to discuss with you again.
Gianfranco