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MathGroup Archive 2006

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Re: General--Different Results

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69447] Re: General--Different Results
  • From: p-valko at tamu.edu
  • Date: Wed, 13 Sep 2006 04:01:00 -0400 (EDT)
  • References: <ee64m2$7jl$1@smc.vnet.net>

If you put
Assumptions -> {a > 0, κ > 0, ν > 0}
into the Integrate, you will get always the same answer.
Regards
Peter

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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