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 tetration exp(z)-1+k tommy1729 Ultimate Fellow Posts: 1,419 Threads: 345 Joined: Feb 2009 02/01/2015, 11:06 PM (01/31/2015, 02:45 AM)sheldonison Wrote: [quote='sheldonison' pid='7609' dateline='1422314910'] where k is a small perturbation constant in the neighborhood of zero... First off, if $k=\ln(ln(b))+1\;\;$ then $s_k(z) = \ln(b)\cdot \text{sexp}\left(\text{slog}(e)-2\right)\;+\;\ln\left(\ln(b)\right)\;$ with some algebraDespite the edit this equation is still wrong. Look , your "z" is on the LHS but not on the RHS. Quote:$\frac{d}{dz}s_k(z) = \frac{d}{dz}s_k(z+1)\;\;$ trivially proven by using the chain rule since $s_k(z+1)=\exp(s_k(z))-1+k$ This is also wrong. sexp'(x+1) = sexp(x+1) sexp'(x). If you say f ' (x) = f ' (x+1) then basicly you say f ' (x) is periodic. Quote:So, this particular point on the tetration curve is the place where the linear approximation piecemeal approximation works best, since ... Considering these mistakes or miscommunications I have trouble following and as a reader am not seduced to do so. Maybe Im harsch but if you ever want to write a paper you will loose the intrest of people after page 1 by these things , if it even gets accepted. As for my opinion , well , considering what I wrote its clear. Also the idea or post seems unfinished and is therefore hard to Judge. Nothing new under the sun till now ? regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread tetration exp(z)-1+k - by sheldonison - 01/27/2015, 12:28 AM RE: tetration exp(z)-1+k - by MphLee - 01/27/2015, 11:18 AM RE: tetration exp(z)-1+k - by sheldonison - 01/27/2015, 03:07 PM RE: tetration exp(z)-1+k - by tommy1729 - 01/30/2015, 07:20 AM RE: tetration exp(z)-1+k - by sheldonison - 01/31/2015, 02:45 AM RE: tetration exp(z)-1+k - by sheldonison - 02/01/2015, 05:57 AM RE: tetration exp(z)-1+k - by tommy1729 - 02/01/2015, 11:16 PM RE: tetration exp(z)-1+k - by sheldonison - 02/02/2015, 05:43 AM RE: tetration exp(z)-1+k - by tommy1729 - 02/01/2015, 11:06 PM RE: tetration exp(z)-1+k - by tommy1729 - 01/31/2015, 09:18 AM

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