File:TetrationQ2r.jpg: Difference between revisions

Latest revision as of 18:55, 11 March 2022

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current	18:55, 11 March 2022		288 × 288 (10 KB)	Maintenance script (talk \| contribs)	== Summary == Importing file

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JPEG file comment	Created by Wolfram Mathematica 5.1

@@ Line 1: / Line 1: @@
-{{Image notes ownworkpro
+== Summary ==
-|Description=Tetration at the base <math>b=\sqrt{2}</math> versus the real argument.
+Importing file
-|CZ username=Dmitrii Kouznetsov
-|Year created=2009
-|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}]]
-.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 *)
-|Other versions=}}