@Pepini That's nice to see.

As mentioned before there can be some GUI sluggishness with high resolution densityplots, which was part of my motivation years ago to get better performance using images (hardware float Arrays). In some older Maple versions the Java JRE was even slower and more memory hobbled, and the Maple GUI densityplot responsiveness more severe.

The GUI does a bit better now, but FYI here's some history:

You cited an old (2019) Question in which I gave this Answer:
   https://www.mapleprimes.com/questions/226790-Is-There-Any-Maple-Code-For-The-domain#answer258068

That in turn has a link to a much older (2011) Post of mine:
   https://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot

I wrote that partially to deal with some examples set in this (2011) Question:
   https://www.mapleprimes.com/posts/95767-Why-With-Mathematica-Not-With-Maple

And that Question cited the following (2011) article, one of whose authors wrote the book you mentioned:
   Phase Plots of Complex Functions: A Journey in Illustration

@Pepini You're welcome.

You can increase the resolution by passing the grid option to the plot3d command, which I showed earlier.

For example,  grid=[201,201]

Note that if you make the grid very fine then the GUI becomes sluggish upon manual rotation of the 3D plot using the mouse. In such cases it can serve one better to figure out an acceptable fixed orientation and pass that in.

@Pepini Your could adjust the following, ie. orientation of the hemispheres, direction, etc.

(The older post you last cited was more about 2D, and running in an older version. For your hemisphere examples it seems more straightforward to plot and color the 3D surfaces directly using more modern coloring options.)

Download col_sphere.mw

If you really want to work with the constructed image, then map the disk to a square, then project onto the hemisphere, then I suppose it could be done. But it seems more complicated.

Also, one of the purposes of using images rather than plots in those older posts was that high resolution plots (eg. 3D surface or 2D density) can stress the GUI far more. The GUI performance benefit of merely embedding images may be lost if the images are used to shade a plotted surface.

Some of the GUI performance discrepancies have lessened witth later releases, due to Java version improvements.

@Pepini This is looking more like a roundabout approach. Rather than have us guess at a projection, it might be better if you were to show the formulaic details of how those images were constructed.

What is the coordinate system, how does their shading depend on that precisely, and how does that correspond to the sphere?

@Djlogan2 The Maple GUI has some neat features as a convenient front end to (usually simpler) computations.

But for well structured work using the Maple programming language as the basis for workflow is far superior to User Interface effects. The full power of the programming language raises the product's power far above what can be done using mainly GUI effects or a fixed set of context-sensitive operations. I recommend the Programming Guide, or the inexpensive and decent Understanding Maple.

@Djlogan2 There are a variety of alternatives, if you throw Equation labels and context-panel operations into the mix.

You can also cook up some alternative syntax. For example using a customized infix operator alongside some Equation Label references (the Equation Labels are shown more nicely, right-justified in the actual Maple GUI),

Download shrtct_eval.mw

That helper routine's name starts with an ampersand (&), which is why it allows for an infix calling sequence. You might name it something else short that you prefer, eg. `&e`

@Carl Love I was confident that I wasn't telling you anything new. Sorry, I could have made it more clear that I was just adding a comment for the OP or other readership.

@ogunmiloro How precisely is that latest attachment different from the original? It looks as if you have accidentallu uploaded the original file again, unchanged.

The proc wrapper approach can work with an `add` call. That can make sense directly.

The `Sum` call conversion can make some sense with an implicit `evalf` acting. (I'm not a huge fan of that kind of thing.)

I don't see why that call to Maple's inert symbolic Sum should translate to that Matlab sum call. They don't directly do the same computation.

@ogunmiloro I have doubts about the correctness of what you write.

You should correct the formulas in a revised worksheet and attach it as followup.

I don't think that it should take four or five postings for you to ask your question with the details present and correct.

@ogunmiloro 

What do you mean by the numerator GAMMA in the terms like

   GAMMA/GAMMA(tau+1)

?

@ogunmiloro Apart from your statement that you want 2D contour plots, I don't see how your latest response answers my questions.

Your sheet already mentioned that tau ranges from 0.2 to 1.0 in query (2). There's no merit in your repeating that. But you still haven't told use what value gamma[1] should take for that plot.

Your sheet already mentioned that gamma[1] ranges from 0.2 to 1.0 in query (3). There's no merit in your repeating that. But you still haven't told use what value tau should take for that plot.

What do you mean by  GAMMA/GAMMA(tau+1)  ?

You have GAMMA used in function calls (ok), but also as a standalone name. What is the numerator supposed to mean, for example in this subexpression:

   GAMMA/GAMMA(tau+1)

?

Also, all three cases's descriptions are incomplete, since numeric values for the remaining parameters are not specified. In case (1) what are values for tau and gamma[1]? In case (2) what is the value of gamma[1]? In case (3) what is the value of tau?

You have also failed to mention what kinds of plots you want? 2D contour plots? 3D contour plots? Something else?

Yes, it's been broken for a few days now.

The flag mechanism also seems broken. Tag deletion also seems broken.