Tetration Forum
Partial Differential Equation for power-towers - Printable Version

+- Tetration Forum (https://math.eretrandre.org/tetrationforum)
+-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)
+--- Thread: Partial Differential Equation for power-towers (/showthread.php?tid=417)



Partial Differential Equation for power-towers - kobi_78 - 02/01/2010

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


RE: Partial Differential Equation for power-towers - mike3 - 02/02/2010

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?