11/21/2015, 05:05 AM
I agree that it is a long-researched problem; trying to find a closed form for super-roots, or anything for that matter.
Using a combination of known facts from the Tetration Ref I collected, I was able to find a simpler expression for the logarithmic power series expansion of \( y = x^{x^x} \) than I remember from before. I think the ideal solution would be to find a recurrence equation similar to the one we know for n-th tetrates. I've attached a short discussion of the things we know that might help in finding a closed form.
Using a combination of known facts from the Tetration Ref I collected, I was able to find a simpler expression for the logarithmic power series expansion of \( y = x^{x^x} \) than I remember from before. I think the ideal solution would be to find a recurrence equation similar to the one we know for n-th tetrates. I've attached a short discussion of the things we know that might help in finding a closed form.