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Change of base formula for Tetration
#27
jaydfox Wrote:You're not factoring in the superlogarithmic constant. You tetrate base b n+mu times, then take the logarithm base a only n times. If base b is greater than base a, then mu will be negative.

You gave the formula for arbitrary . So if is negative I simply choose such that for example (actually I tried and ). Otherwise you have to specify for which x your formula is valid (which makes it clear again that the convergence of your formula wasnt at all "obvious"). Normally the tetration shall be defined for exponents I guess.

However if we can show analyticity it suffices to define it in a small vicinity of some point because from there we can analytically extend it. However the question then is what is and what has the vicinity.
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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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