       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[&#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

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```

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