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