A Version 7 Symbolic Integration Problem
- To: mathgroup at smc.vnet.net
- Subject: [mg94620] A Version 7 Symbolic Integration Problem
- From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
- Date: Wed, 17 Dec 2008 06:56:32 -0500 (EST)
- Organization: University System of Maryland
There is something amiss with symbolic integration under Version 7 that
was not there under Version 6. Here is an integral that arises in the
derivation of Student's t-distribution.
f[x_] = E^(-(x^2/2))/Sqrt[2 \[Pi]]
g[y_] = PDF[ChiSquareDistribution[\[Nu]], y]
h[x_, y_] = f[x] g[y]
F[t_, y_] = h[t Sqrt[y/\[Nu]], y] Sqrt[y/\[Nu]]
Clear[k, y, t, \[Nu]]
TraditionalForm[
k[t_, \[Nu]_] = Assuming[Re[\[Nu]] > -1 && Re[t^2/\[Nu]] > -1, \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\(F[t,
y] \[DifferentialD]y\)\)] // PowerExpand]
Under version 7 everything works until the final step. During execution
the Kernel takes up most of the memory on my computer (4Gb) and then
produces the following message.
No more memory available.
Mathematica kernel has shut down.
Try quitting other applications and then retry.
It is interesting to note that the integral gives the correct answer
under version 6, although it takes a minute or two to get the answer,
but it never uses much memory.
I have referred this to WRI, but got the usual "... sent it to the
developers ... blah blah ... you will be notified ..."
Kevin