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 [split] Understanding Kneser Riemann method sheldonison Long Time Fellow Posts: 664 Threads: 23 Joined: Oct 2008 01/13/2016, 10:55 PM (This post was last modified: 01/13/2016, 10:55 PM by sheldonison.) (01/13/2016, 09:21 PM)andydude Wrote: (01/13/2016, 05:36 PM)sheldonison Wrote: Lets say we have the Schroeder function, and its inverse $S(z)\;\;S^{-1}(z)$ which have corresponding Abel and super functions, $\alpha(z)=\log_L(S(z))\;\;\alpha^{-1}(z)=S^{-1}(L_0+L^z)\;\;$ Notice that for b=e, $\exp(z)\; L_0=L\;\;$ but this is not the case for other bases. So $\alpha^{-1}(z)=S^{-1}(L_0+L^z)$ $S(\alpha^{-1}(z))=L_0+L^z$ $S(z)=L_0+L^{\alpha(z)}$ $S(z)=L_0+S(z)$ $S(z) - S(z) = L_0 = 0$ which means $L_0 = L = 0$? I don't understand.$\alpha^{-1}(z)=S^{-1}(L^z)$ That was a typo; working from the top of my head. Anyway, the inverse of the Schroeder function of L^z is the superfunction. For base-e, it will be around the fixed point, so $S^{-1}(0)=L$. Anyway, the formal Schroeder equation is what you use, at the fixed point of the exponential for base=b. - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread [split] Understanding Kneser Riemann method - by andydude - 01/13/2016, 04:01 PM RE: Should tetration be a multivalued function? - by marraco - 01/13/2016, 05:31 PM RE: Should tetration be a multivalued function? - by sheldonison - 01/13/2016, 05:36 PM RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 06:41 PM RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 09:21 PM RE: Should tetration be a multivalued function? - by sheldonison - 01/13/2016, 10:55 PM RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 09:29 PM RE: Should tetration be a multivalued function? - by sheldonison - 01/13/2016, 10:58 PM

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