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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
POSTED BY: Adam Domjan
3 Replies
Posted 10 years ago
Simpler answer
In[1]:= 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[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 10 years ago
Thank you very much Bill Simpson!
POSTED BY: Adam Domjan
Posted 10 years ago
 In[1]:= 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[4]= ...PlotSnipped...
POSTED BY: Bill Simpson
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