(08/15/2009, 05:00 PM)jaydfox Wrote: In thinking about it, the singularities are trivial to find.You mean *some* singularities?!

Quote:For a=eta, b=e, anywhere that the exp^[n-2](x) is equal to -1, we will have a singularity. The double logarithm of the double exponentiation, in the respective bases, will be 0.These are the singularities induced by .

Quote:This makes me wonder, then: for any given n, there are singularities near the real line, and as n increases, these singularities get arbitrarily close.

Can you make a picture for those that dont currently sit down with a computer algebra system computing exactly this?

Imho the converges to the upper primary fixed point of . So why should they come arbitrarily close to the real axis?