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Visualize q-Pochhammer
QPochhammer has complex behavior near the unit circle 1 which contains a dense subset of essential singularities.
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With[{b = 0.985}, 

 Plot3D[Re[QPochhammer[x + I y]], {x, -b, b}, {y, -b, b}, 

  RegionFunction -> (#1^2 + #2^2 < b^2 &), Mesh -> None, 

  PlotStyle -> Directive[Yellow, Specularity[White, 30]], 

  PlotPoints -> 35]]
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