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Mathematics Mathematica Wolfram Language

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

Posted 11 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 + i2s , 1 , i14s ] 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

POSTED BY: Adam Domjan

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Posted 11 years ago

Simpler answer In[1]:= f[s_] := HypergeometricU[1/2 + I2s, 1, I14s]; Plot[{Re[f[s]], Im[f[s]]}, {s, 4, 6}, PlotRange -> All, WorkingPrecision -> 50] Out[2]= ...PlotSnipped... Should have tried that first, but since you wrote you had already tried extra precision I assumed it was getting confused when probing for points and I went for brute force exact value Table construction and didn't check to see if I could just coax a simple Plot into working correctly. Sorry

POSTED BY: Bill Simpson

Posted 11 years ago

Thank you very much Bill Simpson!

POSTED BY: Adam Domjan

Posted 11 years ago

In[1]:= f[s_] := HypergeometricU[1/2 + I2s, 1, I14s]; 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[4]= ...PlotSnipped...

POSTED BY: Bill Simpson

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