File:ArcGamma.jpg

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Original file(1,188 × 924 pixels, file size: 156 KB, MIME type: image/jpeg)

Summary

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Title / Description


ArcFactorial function at the complex -plane.

The lines of constant and the lines of constant are drawn.
Levels are shown with thick black curves.
Levels are shown with thin blue curves.
Levels are shown with thick blue curves.
Level is shown with thick pink line.
Levels are shown with thick red curves.
Intermediate levels of constant are shown with thin greel curves. The cutline of therange of holomorphizm is shown with dashed black line.

Citizendium author
& Copyright holder


Copyright © Dmitrii Kouznetsov.
See below for licence/re-use information.
Date created


2009
Country of first publication


日本
Notes


code: ArcGamma.jpg/code

The same image can be considered also as plot of ArcGamma finction; in this case, the black curves corresponds to values of the real part 2,3,4.

Other versions


There are similar plots for the logarithm and superlogarithm functions,

Logez02.jpg, Slogez01.jpg

Using this image on CZ


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{{Image|ArcGamma.jpg|right|350px|Add image caption here.}}
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Licensing/Copyright status

This media, ArcGamma.jpg, is licenced under the Creative Commons Attribution-NoDerivs 3.0 Unported License

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File history

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Date/TimeThumbnailDimensionsUserComment
current13:50, 18 January 2009Thumbnail for version as of 13:50, 18 January 20091,188 × 924 (156 KB)Dmitrii Kouznetsov (Talk | contribs){{Image notes ownworkpro |Description=ArcFactorial function at the complex <math>z</math>-plane. The lines of constant <math>u=\Re({\mathrm{ArcFactorial}(z)</math> and the lines of constant <math>v=\Im({\mathrm{ArcFactorial}(z)</math> are drawn.<br> Levels <math>u=1,2,3</math> are shown with thick black curves.<br> Levels <math>u= 0.2,0.4,0.6,0.8, 1.2,1.4,1.6,1.8, 2.2,2.4,2.6,2.8, 3.2,3.4,3.6 </math> are shown with thim blue curves.<br> Levels <math>v=1,2,3</math> are shown with thick blue curves.<br> Level <math>v=0</math> is shown with thick pink line.<br> Levels <math>v=-1,-2,-3</math> are shown with thick red curves.<br> Intermediate levels of constant <math>v</math> are shown with thin greel curves. The cutline of therange of holomorphizm is shown with dashed black line. |CZ username= Dmitrii Kouznetsov |Year created= 2009 |Notes= code: ArcGamma.jpg/code <br> The same image can be considered also as plot of ArcGamma finction; in this case, the black curves corresponds to values of the real part 2,3,4. |Other versions=}}
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