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 Simplified regular tetration bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 05/03/2009, 09:33 AM (05/03/2009, 08:49 AM)andydude Wrote: So is X the inverse of the Schroeder function?Actually I am also somewhat puzzled. I would suggest to always use variable $b$ for the base. In this terminology you wrote: ${}^{y}b = X(\ln({}^{\infty}b), \ln({}^{\infty}b)^y)$ Now ${^\infty b}$ is the fixed point which I denoted with $a$. And $\ln(a)$ is the derivative at the fixed point which I denoted with $c$. So your formula is: ${}^{x}b = X(c, c^x)$ while my formula is: ${^xb}=\eta(c^x)+a$ Your coefficients are polynomials in $c$, while my coefficients are rational functions in $c$ and also use $\ln(b)$. Though both must be equal up to translation. *headscratch* « Next Oldest | Next Newest »

 Messages In This Thread Simplified regular tetration - by andydude - 05/02/2009, 12:13 AM RE: Simplified regular tetration - by bo198214 - 05/02/2009, 08:47 AM RE: Simplified regular tetration - by andydude - 05/03/2009, 08:49 AM RE: Simplified regular tetration - by bo198214 - 05/03/2009, 09:33 AM

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