Is it possible to have a complex nu in ParabolicCylinderD?

Question

I'm trying to recreate a graph from a paper, and the function that I'm plotting involves three separate parabolic cylinder functions that all have a complex Nu value. After getting it all typed out, I end up with an empty plot. I've gone back to basics and have fiddled around with ParabolicCylinderD, and have found that I can plot it no problem with a real Nu, but as soon as I make Nu complex I end up with an empty plot. What am I doing wrong?
Edit:
I'll put in the test code I used while playing with the function to see if it worked, but it's just a case of using a complex input with the function to see if it works.
Plot[ParabolicCylinderD[2,p],{p,0,50}]

That one worked totally fine, got a good plot from it.
Plot[ParabolicCylinderD[2 I,p],{p,0,50}]

This one didn't work at all, got an empty plot as a result.

flinty · Answer

Yes certainly. If you have a fixed complex $nu$ then use ComplexPlot not Plot like so:
ComplexPlot[ParabolicCylinderD[0.3 + 0.2 I, z], {z, -1 - I, 1 + I}]

... or if you still want to use Plot, then take the real and imaginary parts separately:
Plot[{Re[ParabolicCylinderD[0.3 + 0.2 I, x]], 
  Im[ParabolicCylinderD[0.3 + 0.2 I, x]]}, {x, -3, 3}, 
 PlotStyle -> {Directive[Red], Directive[Blue]}]

For $nu=2mathbf{i}$ we have real and imaginary parts quickly decaying towards zero:
Plot[{
  Re[ParabolicCylinderD[2 I, x]],
  Im[ParabolicCylinderD[2 I, x]], 
  Abs[ParabolicCylinderD[2 I, x]]}, {x, 0, 10}, 
 PlotStyle -> {Directive[Red], Directive[Blue], Directive[Thick, Darker@Green]}, 
 PlotRange -> All, 
 PlotLegends -> {"Re", "Im", "Abs"}]

Is it possible to have a complex nu in ParabolicCylinderD?

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