I need to graph the function $$f_s(x)=\frac{1+2x^2-3x^2\Xi(x)}{1-x^2},$$ were $$\Xi(x)= \begin{cases} \frac{1}{\sqrt{1-x^2}}\tanh^{-1}(\sqrt{1-x^2}); & 0\leq x<1\\ \frac{1}{\sqrt{x^2-1}}\tan^{-1}(\sqrt{x^2-1}); & x \geq1 \end{cases}.$$
My effort:
P1 = Plot[(1 + 2 x^2)/(1 - x^2) + (3 x^2 ArcTanh[Sqrt[x^2 - 1]])/\!\(\*SuperscriptBox[\((\*SuperscriptBox[\(x\), \(2\)] - 1)\), \({\*FractionBox[\(3\), \(2\)]}\)]\), {x, 1, 14}, PlotTheme -> "Scientific", PlotStyle -> Black, FrameTicks -> {{{-2, -1.5, -1, 0, 0.5, 1},
None}, {{0, 2, 4, 6, 8, 10, 12, 14}, None}}]
P2 = Plot[(1 + 2 x^2)/(1 - x^2) - (3 x^2 ArcTanh[Sqrt[-x^2 + 1]])/\!\(\*SuperscriptBox[\((\(-\*SuperscriptBox[\(x\), \(2\)]\) + 1)\), \({\*FractionBox[\(3\), \(2\)]}\)]\), {x, 0, 1}, PlotTheme -> "Scientific", PlotStyle -> Black, FrameTicks -> {{{-2, -1.5, -1, 0, 0.5, 1},
None}, {{0, 2, 4, 6, 8, 10, 12, 14}, None}}]
Show[P1, P2]
Tanh
, but in your code you useArcTan
. $\endgroup$ – C. E. Jul 12 '17 at 0:10