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Avoid kernel crash when calculating sum of HypergeometricPFQ functions?

Steven Clark

Posted 7 years ago

Why does the kernel crash and exit when I try to run the last three evaluations in the attached notebook? Does anyone have any suggestions as to how I can get around this obstacle? I'm running Mathematica 11 Home Edition on Ubuntu 16.04 LTS on an Intel i5 processor: Version Number: 11.0.0.0 Platform: Linux x86 (64-bit) Here's an extract of the definition of the function. fSum[y_, imax_] := Block[{i = 1, isum = 0}, While[i <= imax, isum += (HypergeometricPFQ[{3/4 + 1/2 I Im[ZetaZero[i]]}, {1, 7/4 + 1/2 I Im[ZetaZero[i]]}, -(y^2/4)]/(-3 I + 2 Im[ZetaZero[i]]) - HypergeometricPFQ[{3/4 - 1/2 I Im[ZetaZero[i]]}, {1, 7/4 - 1/2 I Im[ZetaZero[i]]}, -(y^2/4)]/( 3 I + 2 Im[ZetaZero[i]])); i++]; 2 I isum] Here's an extract of the evaluation which causes the problem. I can run an evaluation with imax=45, but not with imax=46. Plot[N[fSum[y, 46]], {y, 0, 50}, GridLines -> Automatic, PlotPoints -> 200, MaxRecursion -> 0] Attachments:

Why does the kernel crash and exit when I try to run the last three evaluations in the attached notebook?

Does anyone have any suggestions as to how I can get around this obstacle?

I'm running Mathematica 11 Home Edition on Ubuntu 16.04 LTS on an Intel i5 processor:

Version Number: 11.0.0.0

Platform: Linux x86 (64-bit)

Here's an extract of the definition of the function.

fSum[y_, imax_] := Block[{i = 1, isum = 0},
  While[i <= imax, 
   isum += (HypergeometricPFQ[{3/4 + 1/2 I Im[ZetaZero[i]]}, {1, 
        7/4 + 1/2 I Im[ZetaZero[i]]}, -(y^2/4)]/(-3 I + 
       2 Im[ZetaZero[i]]) - 
      HypergeometricPFQ[{3/4 - 1/2 I Im[ZetaZero[i]]}, {1, 
        7/4 - 1/2 I Im[ZetaZero[i]]}, -(y^2/4)]/(
      3 I + 2 Im[ZetaZero[i]])); i++];
  2 I isum]

Here's an extract of the evaluation which causes the problem. I can run an evaluation with imax=45, but not with imax=46.

Plot[N[fSum[y, 46]], {y, 0, 50}, GridLines -> Automatic, 
 PlotPoints -> 200, MaxRecursion -> 0]

POSTED BY: Steven Clark

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Steven Clark

Posted 7 years ago

Mariusz: Thanks for the reply. Your suggestion to use ListLinePlot seems to have the added benefit that it evaluates much faster than the Plot function.