imported>Dmitrii Kouznetsov |
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| == Summary == | | == Summary == |
| {{Image_Details|user
| | Importing file |
| |description = [[Complex map]] of function [[Filog]].
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| <math>\mathrm{Filog}(z)</math> expresses the [[fixed point]] of [[logarithm]] to base <math>b\!=\!\exp(z)</math>.
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| Another fixed point to the same base can be expressed with
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| <math>\mathrm{Filog}(z^*)^*</math>
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| [[Filog]] is expressed through the [[Tania function]], <math>\displaystyle \mathrm{Filog}(z)= \frac{\mathrm{Tania}\!\big(\ln(z)-1-\mathrm{i}\big)}{-z}</math>
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| <math>f=\mathrm{Filog}(x+\mathrm{i} y)</math> is shown in the <math>x,y</math> plane with
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| levels <math>u=\Re(f)=\mathrm{cont}</math> and
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| levels <math>v=\Im(f)=\mathrm{cont}</math>; thick lines correspond to the integer values.
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| The additional thin gridlines <math>x\!=\!\exp(-1)</math> and <math>x\!=\!\pi/2</math> are drawn. The first of them goes through the branchpoint <math>z=1/\mathrm e</math>, which is the branch point; the second goes through the point
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| <math>z=\pi/2</math>, where the fixed points are </math>\pm \mathrm i</math>.
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = 2012.03.08
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| |pub-country = Japan
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| |notes = I tried to save it as http://en.citizendium.org/wiki/File:FilogmapT.png
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| but it does not load as it is expected..
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| |versions = [[File:FilogmapT.png|30px]] and http://tori.ils.uec.ac.jp/TORI/index.php/File:Filogbigmap100.png
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| }}
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| == Licensing ==
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| {{CC|by|3.0}}
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Latest revision as of 19:57, 11 March 2022
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