Re: Why is the tetration so much harder to extend than the factorial?


What do you mean by whether or not tetration "exists" or
not, anyway? One can come up with plenty of functions that
solve the two main functional equations, the only question is
which of those functions do we use as a suitable extension
to real/complex numbers, like the problem with the gamma
function providing a suitable extension of factorial.


To be of any use in complex analysis, the function should be
analytic. Am I wrong in believing that none of the candidates
for tetration has been proved analytic?

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.

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