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MathGroup Archive 2006

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General--Different Results

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69437] General--Different Results
  • From: aerolapo at hotmail.com
  • Date: Tue, 12 Sep 2006 06:53:37 -0400 (EDT)

I'va got problem in solving this equation,

-((4*Pi*Subscript[ϵ, 0]*n^2*Subscript[k, 0]*A^2)*Abs[ν]*

  Integrate[r^2*BesselJ[ν, κ*r]*BesselJ[ν - 1, κ*r], 
   {r, 0, a}])/((κ*c)*ν)

because sometimes (the first two or three times I calculate it after opening Mathematica) the result is:

-((4^(1 - ν)*a^3*A^2*n^2*Pi*(a*κ)^(2*ν - 1)*abs[ν]*

   HypergeometricPFQ[{ν + 1/2}, {2*ν, ν + 2}, (-a^2)*κ^2]*
   Subscript[k, 0]*Subscript[ϵ, 0])/(c*κ*ν*Gamma[ν]*
   Gamma[ν + 2]))

and some other times: (after two or three identical calculation the result change and it is always this one)

-((2*a^2*A^2*n^2*Pi*Abs[ν]*(ν*BesselJ[ν, a*κ]^2 -

    (ν - 1)*BesselJ[ν - 1, a*κ]*BesselJ[ν + 1, a*κ])*
   Subscript[k, 0]*Subscript[ϵ, 0])/(c*κ^2*ν))

Note that I run exaclty the same procedure in both cases (only the expression on the notebook, I press shift+enter, but if I cancel the result and retype shift+enter it sometimes changes).

I don't know if the two of them are equivalent, but, is it possible there is a mistake and only one of them is correct? Is there a method to test the equivalence? If they are equivalent, which is the rule followed by Mathematica to choose the result to return?

Thank you very much.

Jacopo 

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