I like to see the branch cut of the function:
$$1 - z \ln[(1+z)/z].$$
If I plot it in the complex plane:
Plot3D[Re[1 - (x + I y) Log[(1 + x + I y)/(x + I y)]], {x, -2,
2}, {y, -2, 2}]
The result is:
which shows the brach cut correctly between -1 and 0. How can I get rid of the hole in the picture and have a smooth line as a branch cut rather than a white line discontinuity?
Also the same for contour plot:
With[{z = x + I y},
ContourPlot[Re[1 - z Log[(1 + z)/(z)]], {x, -2, 2}, {y, -2, 2},
Contours -> 40]]
Exclusions -> None
to get rid of the white line. $\endgroup$ – C. E. Aug 18 '19 at 11:08