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Topic: There are still no reports in!
Replies: 5   Last Post: Dec 3, 2011 5:47 PM

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clicliclic@freenet.de

Posts: 978
Registered: 4/26/08
There are still no reports in!
Posted: Nov 26, 2011 4:47 PM
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Hello,

many things have changed on sci.math.symbolic since two years ago:

The rule-based integrator Rubi developed by Albert Rich came along as
did version 8 of Mathematica; the Wolfram Researchers are rumored to be
working on a new integrator and have stopped posting to the group; all
posts by Albert Rich were deleted from the Google archive while Rubi's
executable rule system morphed into a merely human-readable formula
collection; and the regular Cyber-Tester messages have finally ceased as
well.

I doubt that all of these changes are unrelated.

But one thing hasn't changed: there are still no reports in on Martin's
second elementary double integral, as posted in October 2009:

<http://groups.google.com/group/sci.math.symbolic/browse_thread/thread/c42b461e9c9710e3>

<http://mathforum.org/kb/message.jspa?messageID=6872137&tstart=0>

Define:

jxx(x,y,z) := -x*y*(2*(x^2+y^2+z^2)^(3/2) - 2*z^3 - 3*z*(x^2+y^2)) /
((x^2+y^2+z^2)^(3/2)*(x^2+y^2)^2)

jxy(x,y,z) := ((x^2-y^2)*(x^2+y^2+z^2)*((x^2+y^2+z^2)^(1/2) - z) -
z*x^2*(x^2+y^2)) / ((x^2+y^2+z^2)^(3/2)*(x^2+y^2)^2)

Now, what is the simple, elementary result of:

int(int(jxx(x, y-a/2, z) * jxx(x, y+a/2, z) + jxy(x, y-a/2, z) *
jxy(x, y+a/2, z), x, -inf, inf), y, -inf, inf)

where z >= 0? Simple transformations leading to the solution of a
related problem via elementary antiderivates were shown in

<http://groups.google.com/group/sci.math.symbolic/browse_thread/thread/48542f8286f6352e>

<http://mathforum.org/kb/message.jspa?messageID=6477150&tstart=0>

Perhaps somebody wants to give the second double integral another try.
Is your CAS no weakling anymore?

Martin.



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