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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
>
>
> --
>
> Daniel Huber
> Metrohm Ltd.
> Oberdorfstr. 68
> CH-9100 Herisau
> Tel. +41 71 353 8585, Fax +41 71 353 8907
> E-Mail:<mailto:dh at metrohm.com>
> Internet:<http://www.metrohm.com>
>
>

--
Dr J. McKenzie Alexander
Department of Philosophy, Logic and Scientific Method
London School of Economics and Political Science
Houghton Street, London WC2A 2AE




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