Range of complex tetration as real

[Daniel]

Running my tetration code I was reminded that my results for \[^x a \textrm{, where } 1<a<1.444\] have their range on the real line. Do other extensions of tetration work in a similar fashion?

[bo198214]

Running my tetration code I was reminded that my results for \[^x a \textrm{, where } 1<a<1.444\] have their range on the real line. Do other extensions of tetration work in a similar fashion?

As far as I remember the Paulsen continuation has a super small imaginary part on the real axis for those bases. But for those bases there are not much different from regular tetrations out there. The interesting bases are surely \[b>e^{1/e}\] and there is much more variety with different methods.

[Shanghai46]

Running my tetration code I was reminded that my results for \[^x a \textrm{, where } 1<a<1.444\] have their range on the real line. Do other extensions of tetration work in a similar fashion?

With my extention, as long as you're not doing any tetration towards -2 or less, it always gives real outputs with real heights, ONLY if the base is higher than 1. Otherwise my extension do gives complex results.