File:TetrationQ2r.jpg: Difference between revisions
imported>Dmitrii Kouznetsov ({{Image notes ownworkpro |Description=Tetration at the base <math>b=\sqrt{2}</math> versus the real argument. |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[...) |
imported>Caesar Schinas m (Bot: Replace Template:Image_notes_* with Template:Image_Details) |
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{{ | {{Image_Details|user | ||
| | |description = Tetration at the base <math>b=\sqrt{2}</math> versus the real argument. | ||
|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 *) | (* Generator of figure tetrationQ2r.jpg *) | ||
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(* End of Mathematica file. Copyleft 2009 by Dmitrii Kouznetsov *) | (* End of Mathematica file. Copyleft 2009 by Dmitrii Kouznetsov *) | ||
| | |versions = | ||
}} | |||
Revision as of 02:21, 22 June 2009
| Title / Description
|
Tetration at the base versus the real argument. |
|---|---|
| Citizendium author & Copyright holder
|
Copyright © Dmitrii Kouznetsov. See below for licence/re-use information. |
| Date created
|
2009 |
| Country of first publication
|
Please edit this page and add the country of first publication, or note that it is unknown. |
| 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 *) |
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