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Mathematica Graphics


Could anyone tell me how to make Mathematica plot the following function
smoothly?

Wbar[q_,w_]:=w/(4 Sin[q/2]);

Chi[q_,w_]:=
  EllipticF[Pi/2 - ArcSin[Wbar[q,w]], 1/(1-Wbar[q,w]^2)]  /
Sqrt[1-Wbar[q,w]^2];

ChiPlot[q_,w_]:=
  If[(w>2 Sin[q])&&(w < 4 Sin[q/2]), Chi[q,w]/(2 Pi Sin[q/2]),0];

Plot[{ChiPlot[0.025,w]},{w,0.04999,0.050},PlotPoints->200,
  PlotRange->{19.998,20.003}]

If I run the last Plot command, Mathematica always complains about
ChiPlot[w] not being a machine-size real number at some points, and then
it only plots several disconnected lines. I realize the function is
rather `dangerous' but analytically  I expect it  to behave normally
inside the region that I use above, except perhaps at the
boundaries. Anyway, if Mathematica can get the separate lines, why can't
it obtain
the values for points between the lines also?

Much thanks in advance,

David Djajaputra



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