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# Confluent Hypergeometric Function of the 2nd Kind (HypergeometircU[a,b,z])

Posted 10 years ago
 Dear Wolfram Community!Does anyone can help me the following problem:I would like to get the correct value of the following function: f[s]:=HypergeometricU[ 1/2 + i*2*s ,  1 ,  i*14*s ]Plot[ { Re[ f[s] ] , Im[ f[s] ] } , { s, 3, 6 } , PlotRange -> All , PlotStyle -> Thick ]When I plotted the function values it can be seen the the function values for s>4 is not good.I try the MaxExtraPrecision=100,150,500,... command, but it does not help for this. (I don't know why.)Can anyone suggest a solution for this problem?Adam
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Posted 10 years ago
 Simpler answerIn:= f[s_] := HypergeometricU[1/2 + I*2*s, 1, I*14*s];Plot[{Re[f[s]], Im[f[s]]}, {s, 4, 6}, PlotRange -> All, WorkingPrecision -> 50]Out= ...PlotSnipped...Should have tried that first, but since you wrote you had already tried extra precision I assumedit was getting confused when probing for points and I went for brute force exact value Table constructionand didn't check to see if I could just coax a simple Plot into working correctly.Sorry
Posted 10 years ago
 Thank you very much Bill Simpson!
Posted 10 years ago
 In:= f[s_] := HypergeometricU[1/2 + I*2*s, 1, I*14*s]; v = Table[{s, N[f[s], 50]}, {s, 4, 6, 1/100}]; iv = Map[{First[#], Im[Last[#]]} &, v]; Show[  ListPlot[Re[v], PlotRange -> All, Joined -> True, PlotStyle -> Thick],  ListPlot[iv, PlotRange -> All, Joined -> True]  ]  Out= ...PlotSnipped...