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 Tetration extension for bases between 1 and eta dantheman163 Junior Fellow Posts: 13 Threads: 3 Joined: Oct 2009 12/15/2009, 01:01 AM (This post was last modified: 12/15/2009, 01:02 AM by dantheman163.) Upon closer study i think i have found a formula that actually works. ${}^ x b = \lim_{k\to \infty} \log_b ^k({}^ k b (ln(b){}^ \infty b)^x-{}^ \infty b(ln(b){}^ \infty b)^x+{}^ \infty b)$ Also i have noticed that this can be more generalized to say, if $f(x)=b^x$ then $f^n(x)= \lim_{k\to \infty} \log_b ^k( Exp_b^k(x) (ln(b){}^ \infty b)^n-{}^ \infty b(ln(b){}^ \infty b)^n+{}^ \infty b)$ numerical evidence shows this to be true. some plots ${}^x sqrt2$     half iterite of $sqrt2^x$     The graph falls apart at x=4 because $Exp_b^k(4.01)$ diverges as k goes to infinity. thanks. Edit: sorry for the huge pictures « Next Oldest | Next Newest »

 Messages In This Thread Tetration extension for bases between 1 and eta - by dantheman163 - 11/05/2009, 03:00 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/05/2009, 01:44 PM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 11/05/2009, 11:53 PM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/07/2009, 09:31 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/07/2009, 05:11 PM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/07/2009, 08:12 PM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 11/07/2009, 11:30 PM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/08/2009, 02:44 PM RE: Tetration extension for bases between 1 and eta - by mike3 - 11/12/2009, 07:11 PM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 12/15/2009, 01:01 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 12/15/2009, 01:40 AM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 12/15/2009, 01:48 AM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 12/17/2009, 02:40 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 12/17/2009, 10:59 AM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 12/19/2009, 05:06 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 12/19/2009, 10:55 AM

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