File:Lambert W Range.pdf
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Summary
[edit]| Description |
The range of the Lambert W function, showing all branches. The orange curves are images of either the positive or the negative imaginary axis. The black curves are images of the positive or negative real axis (except for the one that intersects −1, which is the image of part of the negative real axis). The purple curve and circle is the image of a small circle around the branch point z=0; the red curves are the images of a small circle around the point z=-1/e. The range of W0 is inside the C-shaped black curve. The range of each of the other branches is a band between two black curves that represent points on the negative real axis (a black curve representing the positive real axis runs through the middle of each such band). |
|---|---|
| Source |
Created in mathematica 9.0 |
| Date |
2017-10-06 |
| Author | |
| Permission (Reusing this file) |
See below.
|
- Other information
ComplexPlot[f_, opts__] := ParametricPlot[{Re[f], Im[f]}, opts]
branch[k_] := {ComplexPlot[
ProductLog[k, -1/E + E^(I t)/10], {t, -\[Pi], \[Pi]},
PlotStyle -> Red],
ComplexPlot[ProductLog[k, E^(I t)/5], {t, -\[Pi], \[Pi]},
PlotStyle -> Purple],
ComplexPlot[ProductLog[k, I E^t], {t, -10, 2000},
PlotStyle -> Orange, PlotRange -> All, PlotPoints -> 1000],
ComplexPlot[ProductLog[k, I E^t], {t, -2000, -10},
PlotStyle -> Orange, PlotRange -> All, PlotPoints -> 1000],
ComplexPlot[ProductLog[k, -I E^t], {t, -10, 2000},
PlotStyle -> Orange, PlotRange -> All, PlotPoints -> 1000],
ComplexPlot[ProductLog[k, -I E^t], {t, -2000, -10},
PlotStyle -> Orange, PlotRange -> All, PlotPoints -> 1000]}
Show[ParametricPlot[{-t Cot[t], t}, {t, -5 \[Pi], 5 \[Pi]},
PlotStyle -> {Thickness[0.002], Black},
Exclusions -> Range[-4, 4, 1]*\[Pi]], branch[0], branch[1],
branch[-1], branch[2], branch[-2], branch[3], branch[-3],
PlotRange -> {{-16, 16}, {-16, 16}}]
Licensing
[edit] | Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. |
   | This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License. |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:24, 6 October 2017 |  | 1,383 × 1,383 (157 KB) | Sławomir Biały (talk | contribs) | Uploading a self-made file using File Upload Wizard |
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