File:FilogmT1000a.jpg

Complex map of function Filog.

$u\!+\!\mathrm i v= \mathrm{Filog} (x\!+\!\mathrm i y)$

Meaning

$z=\mathrm{Filog}(a)$ expresses solution $z$ of equation $\ln(z)/a=z$.

C++ generator of curves

Latex generator of labels

%File filogm.pdf should be generated with code above in order to compile the Latex document below: % <br> \documentclass[12pt]{article} %<br> \usepackage{geometry} %<br> \paperwidth 315pt %<br> \paperheight 216pt %<br> \topmargin -102pt %<br> \oddsidemargin -88pt %<br> \usepackage{graphicx} %<br> \usepackage{rotating} %<br> \newcommand \rot {\begin{rotate}} %<br> \newcommand \ero {\end{rotate}} %<br> \newcommand \rme {\mathrm{e}} %<br> \newcommand \sx {\scalebox} %<br> \begin{document} %<br> \begin{picture}(208,208) %<br> \put(10,10){\includegraphics{filogm}} %<br> \put(4,207){$1$} %<br> \put(0,147){$y$} %<br> \put(4,107){$0$} %<br> \put(-3, 8){$-\!1$} %<br> \put(2, 0){$-\!1$} %<br> \put(108, 0){$0$} %<br> \put(140, 2){\sx{.8}{$1/\rme$}} %<br> \put(209, 0){\sx{1}{$1$}} %<br> \put(264, 2){\sx{.8}{$\pi/2$}} %<br> \put(307, 2){\sx{.9}{$x$}} %<br> \put(185,43){\sx{.8}{\rot{64}$v\!=\!2$ \ero} } %<br> \put(250,49){\sx{.6}{\rot{84}$v\!=\!1.2$ \ero} } %<br> \put(281.5,43){\sx{.8}{\rot{80}$v\!=\!1$ \ero} } %<br> \put(283,161){\sx{.6}{\rot{-40}$v\!=\!0.8$ \ero} } %<br> \put(250,143){\sx{.6}{\rot{60}$u\!=\!0.2$ \ero} } %<br> \put(283,118){\sx{.8}{\rot{35}$u\!=\!0$ \ero} } %<br> \put(284,74){\sx{.6}{\rot{5}$u\!=\!-0.2$ \ero} } %<br> \put(28.4,120){\sx{.7}{\rot{79}$u\!=\!0.6$\ero}} %<br> \put(84.4,113){\sx{.7}{\rot{74}$u\!=\!0.8$\ero}} %<br> \end{picture} %<br> \end{document} %<br>