Became Hot Network Question
3 added 73 characters in body

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]]


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?

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]]


2 added 73 characters in body

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?

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?

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?

1

# To plot branch cut of logarithm

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?