File:TetrationQ2r.jpg: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Caesar Schinas
m (Bot: Replace Template:Image_notes_* with Template:Image_Details)
(== Summary == Importing file)
Tag: Server-side upload
 
Line 1: Line 1:
{{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    =
}}

Latest revision as of 18:55, 11 March 2022

Summary

Importing file

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current18:55, 11 March 2022Thumbnail for version as of 18:55, 11 March 2022288 × 288 (10 KB)Maintenance script (talk | contribs)== Summary == Importing file

You cannot overwrite this file.

The following page uses this file:

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Retrieved from "https://citizendium.org/wiki/index.php?title=File:TetrationQ2r.jpg&oldid=7111"