Re: Integration error
- To: mathgroup at smc.vnet.net
- Subject: [mg108920] Re: Integration error
- From: "J. McKenzie Alexander" <jalex at lse.ac.uk>
- Date: Wed, 7 Apr 2010 03:20:32 -0400 (EDT)
Just a follow-up...
Here's another problem with Mathematica's integration engine: take the PDF for the (0,1) - L=E9vy distribution, shift it 1/4 to the right, then calculate the area under the curve between -1/4 and 0. I get an imaginary answer...
In[41]:== PDF[LevyDistribution[0, 1]][x] /. {x -> (x - 1/4)}
Out[41]== E^(-(1/(2 (-(1/4) + x))))/(Sqrt[2 \[Pi]] (-(1/4) + x)^(3/2))
and
In[42]:== Integrate[
E^(-(1/(2 (-(1/4) + x))))/(
Sqrt[2 \[Pi]] (-(1/4) + x)^(3/2)), {x, -1/4, 0}
]
Out[42]== -I (Erfi[1] - Erfi[Sqrt[2]])
Cheers,
Jason
> Hi Jason,
> looks like a bug to me. You have a rational real integrand without
> poles in R, therefore, the definite integral must be real.
> Please report this bug to Wolfram.
> Daniel
>
>
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> Daniel Huber
> Metrohm Ltd.
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Dr J. McKenzie Alexander
Department of Philosophy, Logic and Scientific Method
London School of Economics and Political Science
Houghton Street, London WC2A 2AE