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 Alternate solution of tetration for "convergent" bases discovered tommy1729 Ultimate Fellow Posts: 1,358 Threads: 330 Joined: Feb 2009 09/14/2010, 11:33 PM (09/14/2010, 10:30 PM)sheldonison Wrote: The period for the regular superfunction, is a somewhat complicated mess. As z->-infinity, the behavior of the regular superfunction is approximated by an exponential. This is the formula I use. $\text{RegularSuper}_{B}(z) = \lim_{n \to \infty} B^{[n](L + {(L\times\ln(B))}^{z-n})}$ The next step, is to figure out what the periodicity is, taking into account because L is a fixed point, then B^L=L. As z -> -infinity, $\text{RegularSuper}(z) = L+{(L\times\log(B))}^z$ $\text{Period}=2Pi*I/\log(L*\log(B))$ $\text{Period}=2Pi*i/(\log(L) + \log(\log(B)))$ substitute: $L=B^L$, $\log(L)=\log(B^L)$, $\log(L)=L\times\log(B)$ $\text{Period}=2Pi*i/(L\times\log(B) + \log(\log(B)))$ hmm i was looking for the superduper general case of how to find the period of the regular super of any function... i believe such a formula exists .. perhaps even mentioned before ... perhaps even by you ... perhaps in thread " using sinh " ? i seem to have such a kind of deja vu ... « Next Oldest | Next Newest »

 Messages In This Thread Alternate solution of tetration for "convergent" bases discovered - by mike3 - 09/13/2010, 11:30 AM RE: Alternate solution of tetration for "convergent" bases discovered - by tommy1729 - 09/13/2010, 11:20 PM RE: Alternate solution of tetration for "convergent" bases discovered - by mike3 - 09/14/2010, 01:50 AM RE: Alternate solution of tetration for "convergent" bases discovered - by tommy1729 - 09/14/2010, 12:26 PM RE: Alternate solution of tetration for "convergent" bases discovered - by mike3 - 09/14/2010, 11:04 PM RE: Alternate solution of tetration for "convergent" bases discovered - by sheldonison - 09/14/2010, 11:36 PM RE: Alternate solution of tetration for "convergent" bases discovered - by mike3 - 09/15/2010, 02:18 AM RE: Alternate solution of tetration for "convergent" bases discovered - by sheldonison - 09/13/2010, 11:45 PM RE: Alternate solution of tetration for "convergent" bases discovered - by mike3 - 09/14/2010, 01:53 AM RE: Alternate solution of tetration for "convergent" bases discovered - by sheldonison - 09/14/2010, 02:18 PM RE: Alternate solution of tetration for "convergent" bases discovered - by tommy1729 - 09/14/2010, 07:41 PM

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