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Change of base formula for Tetration
#32
bo198214 Wrote:Sorry Jay we dont speak about the same thing.
You ask me why I assume .
I answered: because your formula does not converge for some x if we allow .
You answered: that I didnt pay attention to .
I answered: there are despite values of x for which it doesnt converge.

And I can not relate your current answer to this problem.
To express it in formulas and numbers:
Your definition: For a given tetration for base compute another tetration for base by the formula

where is chosen accordingly that .

This formula is equivalent to


By definition , so if I chose
then .
If I now compute the sequence

say for bases and I get for :


For me this means your formula gives no result in this case.
Well, yeah, if mu_b(a) >= 2, then you can't solve for a^^(-mu_b(a)). I still don't see why this is a problem.

For a=3.0, b=1.5, the constant mu_b(a) is going to be something in the neighborhood of 10. So, yeah, if you try to set x=-10 or thereabouts, it's not going to converge properly.
~ Jay Daniel Fox
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Messages In This Thread
Change of base formula for Tetration - by jaydfox - 08/12/2007, 06:39 AM
RE: Parabolic Iteration - by jaydfox - 08/15/2007, 09:19 PM
RE: Parabolic Iteration - by bo198214 - 08/15/2007, 09:30 PM
RE: Parabolic Iteration - by jaydfox - 08/15/2007, 11:41 PM
RE: Parabolic Iteration - by bo198214 - 08/16/2007, 08:17 AM
RE: Parabolic Iteration - by jaydfox - 08/16/2007, 05:51 PM
RE: Parabolic Iteration - by bo198214 - 08/16/2007, 06:40 PM
RE: Parabolic Iteration - by jaydfox - 08/16/2007, 09:47 PM
RE: Parabolic Iteration - by bo198214 - 08/16/2007, 10:07 PM

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