I'm trying to plot two branches of the complex multi-valued function: (In a previous post, Mathematica finds the branch cut of the following function between -1 and 0)

$1-z\ln[(1+z)/z]$.

So, for the real parts of the two sheets, I have:

Plot3D[{Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y])], 
Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y] - 
I 2 Pi)]}, {x, -2, 2}, {y, -3, 3}, BoxRatios -> {1, 1, 1.5}, 
PlotRange -> All, PlotPoints -> 50, Mesh -> 30, 
MeshFunctions -> {Im[Log[#1 + I #2]] &, Re[Log[#1 + I #2]] &}, 
ImageSize -> Large, ColorFunction -> mycolor]

which as expected the two sheets are connected through the branch cut between -1 and 0 on the x-axis:

However, the pictures shows another branch cut between -2 and -1. How come?

I'm trying to plot two branches of the complex multi-valued function: (In a previous post - linked above-, Mathematica found the branch cut of the following function between -1 and 0)

$1-z\ln[(1+z)/z]$.

So, to plot the real parts of the two sheets, we have:

Plot3D[{Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y])], 
Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y] - 
I 2 Pi)]}, {x, -2, 2}, {y, -3, 3}, BoxRatios -> {1, 1, 1.5}, 
PlotRange -> All, PlotPoints -> 50, Mesh -> 30, 
MeshFunctions -> {Im[Log[#1 + I #2]] &, Re[Log[#1 + I #2]] &}, 
ImageSize -> Large, ColorFunction -> mycolor]

which as expected the two sheets are connected through the branch cut between -1 and 0 on the x-axis:

However, the pictures shows another branch cut between -2 and -1. How come?

I'm trying to plot two branches of the complex multi-valued function: (In a previous post, Mathematica finds the branch cut of the following function between -1 and 0)

$1-z\ln[(1+z)/z]$.

So, for the real parts of the two sheets, I have:

Plot3D[{Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y])], 
Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y] - 
I 2 Pi)]}, {x, -2, 2}, {y, -3, 3}, BoxRatios -> {1, 1, 1.5}, 
PlotRange -> All, PlotPoints -> 50, Mesh -> 30, 
MeshFunctions -> {Im[Log[#1 + I #2]] &, Re[Log[#1 + I #2]] &}, 
ImageSize -> Large, ColorFunction -> mycolor]

which as expected the two sheets are connected through the branch cut between -1 and 0 on the x-axis:

However, the pictures shows another branch cut between -2 and -1. How come?

I'm trying to plot two branches of the complex multi-valued function: (In a previous post, Mathematica finds the branch cut of the following function between -1 and 0)

$1-z\ln[(1+z)/z]$.

So, for the real parts of the two sheets, I have:

Plot3D[{Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y])], 
Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y] - 
I 2 Pi)]}, {x, -2, 2}, {y, -3, 3}, BoxRatios -> {1, 1, 1.5}, 
PlotRange -> All, PlotPoints -> 50, Mesh -> 30, 
MeshFunctions -> {Im[Log[#1 + I #2]] &, Re[Log[#1 + I #2]] &}, 
ImageSize -> Large, ColorFunction -> mycolor]

which as expected the two sheets are connected through the branch cut between -1 and 0 on the x-axis:

However, the pictures shows another branch cut between -2 and -1. How come?