When you plot this equation implicitly, you get something really weird. You can see $x^2 - y = 0$ in there, but why do you see a noisy $y^2 - x = 0$ on the side? My guess is that it is a rounding error in the plotting engine.
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2If you graph the right hand side you can see where the "noise" is coming from. – jamisans Mar 05 '14 at 18:47
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These are rounding errors. In those regions, the function is going from an extremely large positive number, to an extremely large negative number. The software is assuming that there must be a zero somewhere in between, and it just doesn't have the numerical resolution to find it.
This does bring up an interesting point though, the parts where the fuzzy line intersect $x^2 - y = 0$ need to be treated as special cases, since the series wants to diverge from one direction, but want to be zero in the numerator. We cannot conclude directly that graph exists at these points.
cnick
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