On Tuesday, 1 July 2014 04:47:13 UTC+1, Christopher J. Henrich  wrote:   
   > In article <1f546b5d-fa4f-413e-9c10-1a9a15a3543b@googlegroups.com>,   
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   > > On Monday, 30 June 2014 21:36:18 UTC+1, pauland...@gmail.com  wrote:   
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   > > > On Monday, 30 June 2014 20:22:55 UTC+1, Axel Vogt  wrote:   
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   > > > > On 30.06.2014 20:01, paulandrewbird@gmail.com wrote:   
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   > > > > > integral( exp( a*x^4+4*b*x^3*y+6*c*x^2*y^2+4*d*x*y^3+e*y^4)   
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   > > > > > ,x=-infty..infty, y=-infty..finty)   
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   > > > > > I'm guessing it's going to be in the form 1/P(a,b,c,d,e)^(1/8) where   
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   > > > > > is a 4th degree polynomial in the coefficients of the quartic.   
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   > > > > > My guess is that P is the discriminant of the polynomial but that is   
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   > > > > > just a guess.   
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   > > > > what do you get and expect if integrand = exp(+-x^2*y^2) ?   
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   > > > Well that would be pi.   
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   > > Sorry no I was thinking of exp(-x^2-y^2). I'm not sure your example   
   converges. What's your point?   
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   > Axel's question concerns an example of your proposed general result.   
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   > (A) True, it may not converge. If it doesn't, this has implications for   
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   > whether your conjecture needs repair.   
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   > (B) If it does converge, you can probably find its value. See if that   
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   > offers a counterexample to your conjecture.   
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   > I don't see any conditions on the signs of the coefficients of your   
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   > quadric. I wonder if you have assumed that the quadric is negative   
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   > definite.   
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   > --   
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   > Chris Henrich    
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   > "Now that I have cleared up my initial confusion, I feel I am confused on a   
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   > much higher plane, and about more significant issues."   
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   >  -- Earliest known sighting: Kelley, "The Workshop Way of Learning", 1951   
      
   The only conditions are that a<0 and e<0.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)