05/14/2015, 06:55 PM
Im reminded of my old tommy's tetration constant.
TT constant for short or now maybe Tommy-Sheldon base constant.
Anyway the issue is that to make the periodicity stronger we make sure the fixpoint and period work together.
Thus im(fix) = im(period)
Exp(a z) = z
Im(z) = 2 pi / a
Then slog base exp(a) has all its singularities lined up with the desired asymptotic period.
Isn't that Nice ?
I think i talked about closed forms for a and exp(a) but I do not remember the results if any. I think it was not here.
A closed form would be appreciated.
Lambert-W ? Contour integral representation ? Nice taylor series ? Tommy-kouznetsov expansion ??
Btw I wonder how many constants are defined in this forum/tetrarion.
Regards
Tommy1729
TT constant for short or now maybe Tommy-Sheldon base constant.
Anyway the issue is that to make the periodicity stronger we make sure the fixpoint and period work together.
Thus im(fix) = im(period)
Exp(a z) = z
Im(z) = 2 pi / a
Then slog base exp(a) has all its singularities lined up with the desired asymptotic period.
Isn't that Nice ?
I think i talked about closed forms for a and exp(a) but I do not remember the results if any. I think it was not here.
A closed form would be appreciated.
Lambert-W ? Contour integral representation ? Nice taylor series ? Tommy-kouznetsov expansion ??
Btw I wonder how many constants are defined in this forum/tetrarion.
Regards
Tommy1729
