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