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, Îº > 0, Î½ > 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[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 > > 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]]