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MathGroup Archive 2006

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Re: General--Different Results

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69445] Re: General--Different Results
  • From: dimmechan at yahoo.com
  • Date: Wed, 13 Sep 2006 04:00:56 -0400 (EDT)
  • References: <ee64m2$7jl$1@smc.vnet.net>

Hello.

***My version of Mathematica does not recognise the character ϵ,
 below. So I replace it with m.

-((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)


$Version
5.2 for Microsoft Windows (June 20, 2005)

***Evaluating the integral I get a conditional result (as it shoulb be
since your integral depends on parameters)

-((4*Pi*Subscript[m, 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) //Timing

{30.141000000000002*Second, (-4*a*A^2*n^2*Pi*Abs[ν]*If[Im[1/(a*κ)] >=
1 || 1 + Im[1/(a*κ)] <= 0 || Im[1/(a*κ)] == 0 ||
     Re[1/(a*κ)] != 0, (a*(a*κ)^(2*ν)*HypergeometricPFQ[{1/2 + ν},
{2*ν, 2 + ν}, -(a^2*κ^2)])/
     (4^ν*κ*Gamma[ν]*Gamma[2 + ν]), Integrate[a^2*r^2*BesselJ[-1 +
ν, a*r*κ]*BesselJ[ν, a*r*κ], {r, 0, 1},
     Assumptions ->  !(Im[1/(a*κ)] >= 1 || 1 + Im[1/(a*κ)] <= 0 ||
Im[1/(a*κ)] == 0 || Re[1/(a*κ)] != 0)]]*
   Subscript[k, 0]*Subscript[m, 0])/(c*κ*ν)}

***It would be very helpful if you give more information about your
parameters.

Cheers
Dimitris

aerolapo at hotmail.com wrote:
> I'va got problem in solving this equation,
>
> -((4*Pi*Subscript[&#1013;, 0]*n^2*Subscript[k, 0]*A^2)*Abs[&#957;]*
>
>   Integrate[r^2*BesselJ[&#957;, &#954;*r]*BesselJ[&#957; - 1, &#954;*r],
>    {r, 0, a}])/((&#954;*c)*&#957;)
>
> because sometimes (the first two or three times I calculate it after opening Mathematica) the result is:
>
> -((4^(1 - &#957;)*a^3*A^2*n^2*Pi*(a*&#954;)^(2*&#957; - 1)*abs[&#957;]*
>
>    HypergeometricPFQ[{&#957; + 1/2}, {2*&#957;, &#957; + 2}, (-a^2)*&#954;^2]*
>    Subscript[k, 0]*Subscript[&#1013;, 0])/(c*&#954;*&#957;*Gamma[&#957;]*
>    Gamma[&#957; + 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[&#957;]*(&#957;*BesselJ[&#957;, a*&#954;]^2 -
>
>     (&#957; - 1)*BesselJ[&#957; - 1, a*&#954;]*BesselJ[&#957; + 1, a*&#954;])*
>    Subscript[k, 0]*Subscript[&#1013;, 0])/(c*&#954;^2*&#957;))
>
> 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
>
> Link to the forum page for this post:
> http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=Special:Forum_ViewTopic&pid=13453#p13453
> Posted through http://www.mathematica-users.org [[postId=13453]]


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