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Partial Differential Equation for power-towers
#1
Hi, I found a pde for power towers of any height.

The equation is as following:

Define




And



Where



Then every satisfies:



I don't understand anything about pdes so I don't know if this says any thing, but I wanted to share it with you guys.

I guess we can somehow use this equation to extend natural iteration monomial for larger bases, but I don't really know.

Kobi
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#2
Hmm. Well if this is the case, then could that mean that there may be a continuum of solutions? If so, could that allow us to define for real and complex values of , thereby yielding for such heights?
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