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Comparing the Known Tetration Solutions
#17
Well, I've prepared some graphs in the hope that I can address the question about my super-logarithm extension. The question was "are you sure?" about my super-logarithm definition not working for bases between . My only answer is to look at the graphs.

These are some graphs of the first three coefficients of the super-logarithm, i.e. the Abel function of . In each graph there are multiple curves, each curve corresponds to a specific approximation; the approximations shown are roughly and the independant axis represents the base . What follows are graphs of as functions of b for for the functional equation with .

  1. A_1(b)
  2. A_2(b)
  3. A_3(b)

As you can see, when the base is between , although the matrix equation has a solution, the solutions (coefficients) do not seem to converge. This is what leads me to beleive that my super-logarithm definition will only work for .

Andrew Robbins
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Messages In This Thread
RE: Comparing the Known Tetration Solutions - by andydude - 08/22/2007, 11:28 PM
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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