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regular tetration at b=e^(-e)

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regular tetration at b=e^(-e)
mike3 Offline
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#2
09/27/2009, 12:52 AM
I've heard that the series obtained for \( f^t(z) \) for \( f(z) = u^z - 1 \) with respect to z at z = 0 do not converge but diverge and diverge very strongly. I suspect this is because at fractional z (iteration number), the fixed point z = 0 is also a branch point at such iteration numbers ("heights", though I prefer to reserve that term for only referring to the second parameter of tetration), and so f is not analytic there. I'm not sure if or how this would carry over to/affect the Schroeder function.
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Messages In This Thread
regular tetration at b=e^(-e) - by bo198214 - 09/26/2009, 09:25 PM
RE: regular tetration at b=e^(-e) - by mike3 - 09/27/2009, 12:52 AM
RE: regular tetration at b=e^(-e) - by bo198214 - 09/27/2009, 06:21 AM
RE: regular tetration at b=e^(-e) - by mike3 - 09/27/2009, 10:24 PM
RE: regular tetration at b=e^(-e) - by Gottfried - 01/11/2010, 12:51 PM
RE: regular tetration at b=e^(-e) - by Gottfried - 08/23/2010, 05:45 PM

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