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Integration of Oscillating Function

  • To: mathgroup at
  • Subject: [mg18445] Integration of Oscillating Function
  • From: Christian Honeker <xian at>
  • Date: Wed, 7 Jul 1999 00:11:31 -0400
  • Sender: owner-wri-mathgroup at

Mathematica Users!

I am attempting to integrate the following function:

function[x_] :=

in the follow manner:

integratedfunction[x_] := (0.00525/(Pi*x^2)) * NIntegrate[function[x_],
{u,0,Infinity}, WorkingPrecision -> 50, MaxRecursion -> 18, MinRecursion
-> 3, AccuracyGoal -> 10]

where u is the integrand and x varies between 0.0001 and 1.

Mathematica responds with a complaint about the WorkPrecision criteria
not being met,
but still finds a solution.
The solution, however, depends strongly on the integration limits (i.e.
it is unstable). For example,
integration of function[0.0001] should result in zero. A plot of
vs. u makes this clear. Depending on the integration range, however,
finds values of integratedfunction[0.0001] between 0 and 65. The
solution for values
of x > 0.006 are correct, however. This is because the oscillation of
decreases rapidly as x increases.

I am hoping that by making Mathematica aware that the function
oscillates strongly,
it can then perform the integration correctly. Setting the option
Methods -> Oscillatory
does not seem to work.

Can anyone help me?


I am performing photon correlation spectroscopy (PCS) on complex fluids.
(above) has its origin in the inverse Laplace transformation of the
(KWW) function. The integration needs to be performed in order to
determine the
distribution of relaxation times which correlate with the size of my
I find that the size distribution (integratedfunction[x_]) has the
correct form
for x > 0.006 (see above). I would like to determine the other half of
size distribution (x < 0.006), however.

Thank you very much for any tips that you can provide!

Michael Bockstaller
Max Planck Institute for Polymer Research

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