Re: Integration error

• To: mathgroup at smc.vnet.net
• Subject: [mg108921] Re: Integration error
• From: dh <dh at metrohm.com>
• Date: Wed, 7 Apr 2010 03:20:43 -0400 (EDT)

Hi Jason,
here the integrand is a complex function
In your case, the trouble maker is the factor:
(-(1/4) + x)^(-3/2);
this is clearly imaginary for x<1/4
Daniel

On 06.04.2010 15:47, J. McKenzie Alexander wrote:
> 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
>
>
>
>
>
>

--
Daniel Huber
Metrohm AG