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