Comparing the Known Tetration Solutions
#22
@Jay
Wow, this is indeed interesting.
I mean theoretically it is clear that \( h(x):=f^{-1}(g(x))-x \) must have period 1 for two (strictly increasing continuous) solutions \( f \) and \( g \) of \( \phi(x+1)=F(\phi(x)) \).

Because \( h(x+1)=f^{-1}(g(x+1))-(x+1)=f^{-1}(F(g(x))-(x+1)=f^{-1}(g(x))+1-(x+1)=h(x) \).

But to see it as graphs is another thing Smile.
And I would think that it is in no way a sinus wave. However the periodic analytic functions can built by Fourier series.


Messages In This Thread
RE: Comparing the Known Tetration Solutions - by bo198214 - 08/29/2007, 07:48 AM
RE: computing the iterated exp(x)-1 - by andydude - 08/17/2007, 11:20 PM
RE: computing the iterated exp(x)-1 - by jaydfox - 08/17/2007, 11:38 PM
RE: computing the iterated exp(x)-1 - by bo198214 - 08/17/2007, 11:45 PM
RE: computing the iterated exp(x)-1 - by jaydfox - 08/18/2007, 12:19 AM
RE: computing the iterated exp(x)-1 - by bo198214 - 08/18/2007, 08:19 AM
RE: computing the iterated exp(x)-1 - by andydude - 08/18/2007, 09:35 AM
RE: computing the iterated exp(x)-1 - by bo198214 - 08/18/2007, 11:59 AM
RE: computing the iterated exp(x)-1 - by jaydfox - 08/18/2007, 03:49 PM
RE: computing the iterated exp(x)-1 - by jaydfox - 08/19/2007, 12:50 AM

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