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Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation
#6
(10/13/2009, 09:47 PM)Base-Acid Tetration Wrote: Theorem. There exists no entire pentation pen_b(z), for b>1, such that pen(0) = 1.

Either you have to specify that pen must use the principal branch of tetration (the cut is nothing god given, its just a choice to our human preference; the real function lives on Riemann manifolds), or you have to modify your proof and use the singularities of tetration at integers <=-2 (and show before that indeed every tetration has singularities there).
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RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by bo198214 - 10/15/2009, 05:01 PM

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