• 1 Vote(s) - 5 Average
• 1
• 2
• 3
• 4
• 5
 Inverse super-composition Xorter Fellow Posts: 93 Threads: 30 Joined: Aug 2016 01/12/2017, 04:19 PM Okey, I have found something looking like the solution. I feel I am closer than ever before. For the following functional equation $2x ^{oN} = exp(x)$ my method gives: $N = 0.5250548915-0.2859572213x+0.3455886342x^2-0.0759083804x^3+0.0201418181x^4-0.0045151851x^5+0.0006517298x^6+...$ Let us check it: $2x ^{o0.5250548915-0.2859572213x+0.3455886342x^2-0.0759083804x^3+0.0201418181x^4-0.0045151851x^5+0.0006517298x^6+...}$ looks like sg like the exoponential function. Of course, because at x=0 exp x = 1, then x2^n will never go up to 1, so in the reals there is no more beautiful solution for N like mine, I think or I am wrong, ain't I? What do you think, is this function correct? Or is there better? Xorter Unizo Xorter Fellow Posts: 93 Threads: 30 Joined: Aug 2016 05/26/2018, 12:00 AM Hi here, again! I have been thinking about functional logarithm, and I coded it in pari/gp in this way: Code:D(f,n)={if(n>0,return(D(deriv(f),n-1)),return(f));}; M(f,n)=matrix(n,n,j,k,1/(k-1)!*subst(D(x*0+f^(j-1),k-1),x,0)); T(A,n)=sum(k=1,n,A[2,k]*x^(k-1)); inv(f,n)=T(M(f,n)^-1,n); Ln(A,n)=sum(k=1,n,(-1)^(k+1)*(A-1)^k/k); olog(f,g,n)=T(Ln(M(f,n),n^2)/(0.1^n+Ln(M(g,n),n^2))); M is the Carleman-matrix, T is a generated taylor-series from the M matrix. Ln is log of a quadratic matrix. And olog is the functional logarithm: olog(f(x),(f^og(x))(x)) = g(x), but somewhy it is not working. E. g. olog(2x,x*2^(2x),100...) = 2x. Could help me? Thank you very much! Xorter Unizo « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post inverse supers of x^3 tommy1729 0 61 06/12/2022, 12:02 AM Last Post: tommy1729 Consistency in the composition of iterations Daniel 9 303 06/08/2022, 05:02 AM Last Post: JmsNxn Improved infinite composition method tommy1729 5 2,201 07/10/2021, 04:07 AM Last Post: JmsNxn Composition, bullet notation and the general role of categories MphLee 8 4,106 05/19/2021, 12:25 AM Last Post: MphLee Is bugs or features for fatou.gp super-logarithm? Ember Edison 10 16,349 08/07/2019, 02:44 AM Last Post: Ember Edison Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 17,258 06/10/2019, 04:29 AM Last Post: Ember Edison Inverse Iteration Xorter 3 7,371 02/05/2019, 09:58 AM Last Post: MrFrety The super 0th root and a new rule of tetration? Xorter 4 9,588 11/29/2017, 11:53 AM Last Post: Xorter Solving tetration using differintegrals and super-roots JmsNxn 0 3,844 08/22/2016, 10:07 PM Last Post: JmsNxn The super of exp(z)(z^2 + 1) + z. tommy1729 1 5,170 03/15/2016, 01:02 PM Last Post: tommy1729

Users browsing this thread: 2 Guest(s)