fd[w_, k_] := (-27 I + w (-12 + w (-18 I + 5 w)) + (27 I + 12 w + w^3) Cos[k])/ (-81 I + w (24 + w (-12 I + 5 w)) + (81 I + w (-24 + w (-6 I + w))) Cos[k]); F[e_] := Sqrt[(1 + Sqrt[1 + e^2])/ (2 Sqrt[1 + e^2])] Exp[(1 - Sqrt[1 + e^2])/2]; f[e_] := 1/2 (1 - Sqrt[1 + e^2] + Log[(1 + Sqrt[1 + e^2])/2]); as[w_, k_] := F[2 k /w]/F[0] Exp[I w (f[2 k /w] - f[0])]; ex[w_, k_] := Hypergeometric0F1[1 - (1 + I w)/2, -k^2/4]; Needs["Graphics`Legend`"]; plarg[w_] := Plot[{-Arg[ex[w, k]], -Arg[as[w, k]], -Arg[fd[w, k]]}, {k, 0, Pi}, Frame->True,PlotLabel->SequenceForm["Phase for frequency=",w], FrameLabel->{"Wavenumber (radians)",None,None,None}, PlotLegend->{"Exact","Asymptotic","Finite-difference"}, LegendPosition->{-0.7,0.2}, LegendSize->{0.9,0.3}, PlotStyle->{{GrayLevel[0.5],Dashing[{0.01}]}, {GrayLevel[0.5],Dashing[{0.03}]}, {}}]; Show[GraphicsArray[{plarg[1], plarg[10]}],AspectRatio->1/(2 GoldenRatio)]; Display["junk_ma.eps",%,"EPS",ImageSize->864];
