0
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I mean the result of

ComplexPlot3D[Sin[z]/MittagLefflerE[10,z],{z,-1-I, 8 + I},Exclusions->None, PlotPoints -> 50]

enter image description here

Its blow-up

ComplexPlot3D[Sin[z]/MittagLefflerE[10, z],{z,-1 - I, 4 + I},Exclusions -> None,PlotPoints -> 100]

enter image description here

does not live up to expectations though takes a lot of time. The Mittag-Leffler function is an entire function without any singularities.

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  • $\begingroup$ The result of ComplexPlot[Sin[z]/MittagLefflerE[10, z], {z, -1 - I, 4 + I}, Exclusions -> None, PlotPoints -> 100] is alright. $\endgroup$ – user64494 Feb 23 at 20:56
4
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Use arbitrary-precision rather than machine precision by specifying the WorkingPrecision.

Clear["Global`*"]

$Version

(* "12.2.0 for Mac OS X x86 (64-bit) (December 12, 2020)" *)

ComplexPlot3D[Sin[z]/MittagLefflerE[10, z], {z, -1 - I, 8 + I}, 
 Exclusions -> None, PlotPoints -> 50, WorkingPrecision -> 15]

enter image description here

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    $\begingroup$ Thank you. ComplexPlot3D[Sin[z]/MittagLefflerE[10, z], {z, -1 - I, 4 + I}, Exclusions -> None, WorkingPrecision -> 15] produces a nice plot on a fresh kernel on my comp during approximately 20 minutes. The resources of my comp are not exhausted. $\endgroup$ – user64494 Feb 23 at 21:25
  • $\begingroup$ On my laptop with a fresh kernel and using the code in your comment, the AbsoluteTiming was less than 4 minutes. $\endgroup$ – Bob Hanlon Feb 23 at 21:34

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