File:TetrationQ2r.jpg: Difference between revisions

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imported>Caesar Schinas
m (Bot: Replace Template:Image_notes_* with Template:Image_Details)
(== Summary == Importing file)
Tag: Server-side upload
 
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{{Image_Details|user
== Summary ==
|description  = Tetration at the base <math>b=\sqrt{2}</math> versus the real argument.
Importing file
|author      = {{#if:Dmitrii Kouznetsov|[[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]}}
|date-created = 2009
|pub-country  =
|notes        = The source used to generate the figure:
(* Generator of figure tetrationQ2r.jpg *)
 
b=Sqrt[2]
RGB[x_,y_,z_]=RGBColor[x,y,z]
M=9
f=2-y+Sum[A[n]*y^n,{n,2,M}]
g=Series[ReplaceAll[f,y\[Rule]y*Exp[q]],{y,0,M}]
h=Simplify[Series[Exp[Log[b]*f],{y,0,M}]]
u=g-h
c1=Coefficient[u,y]
s1=Solve[c1\[Equal]0,q]
s11=Extract[s1,1]
Q=ReplaceAll[q,s11]
v[1]=Simplify[ReplaceAll[u,s11]]
For[i=2,i<M,
  s[i]=Coefficient[v[i-1],y^i];
  t[i]=Extract[Solve[s[i]\[Equal]0,A[i]],1];
  Print[t[i]];
  v[i]=ReplaceAll[v[i-1],t[i]];
  i++]
a[0]=2;
a[1]=-1;
For[i=2,i<M, a[i]=N[ReplaceAll[A[i],t[i]],18] ;i++]
For[i=0,i<M, Print[a[i]] ;i++]
F[z_]=Simplify[Sum[a[i]*Exp[Q*i*z],{i,0,M-1}]]
Plot[F[z],{z,-1,2}];
H[1,z_]=Log[F[z+1]]/Log[b]
For[i=2,i<14, H[i,z_]=Log[H[i-1,z+1]]/Log[b];i++]
Plot[{H[11,z]-H[12,z]},{z,-.5,2},PlotRange\[Rule]All];
z12=ReplaceAll[z,FindRoot[H[12,z]\[Equal]1,{z,-.5,1}]]
                                                                                                                                 
1.251551478822122`
                                                                                                                                 
J[z_]=H[12,z12+z]
                                                                                                                                 
P=Plot[{-z,J[z]},{z,-1.99,4},AspectRatio\[Rule]Automatic,
      GridLines\[Rule]{{-2},{2}},PlotRange\[Rule]{{-2,4},{-4,2}}];
                                                                                                                                 
Export["tetrationQ2r.jpg",P]
 
(* End of Mathematica file. Copyleft 2009 by Dmitrii Kouznetsov *)
|versions    =
}}

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