Re: How to define a specific definite integral result in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg125465] Re: How to define a specific definite integral result in Mathematica*From*: nanobio9 <kuokan.liang at gmail.com>*Date*: Thu, 15 Mar 2012 00:25:03 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jjmv02$cf1$1@smc.vnet.net>

On 3=E6=9C=8813=E6=97=A5, =E4=B8=8B=E5=8D=884=E6=99=8203=E5=88=86, Antonio = Alvaro Ranha Neves <ane... at gmail.com> wrote: > Dear Mathematica users, > > I'd like to use the following integral for symbolic computation, > > Integrate[ > Sin[a] Exp[I r Cos[b] Cos[a]] LegendreP[n, m, Cos[a]] BesselJ[m, > r Sin[b] Sin[a]], {a, 0, \[Pi]}] > > whose result is > > 2 I^(n - m) LegendreP[n, m, Cos[b]] SphericalBesselJ[n, r] > > is there a way to make Mathematica "learn" this result, so that I can work with symbolic computation of the integrand? > > Thanks, > Antonio I hope that I got your question correctly. If you want to manipulate any of {I, n, m, b, r} later, you can just say myIntegral[ I_, n_, m_, b_, r_]:= Integrate[what you did] Later you can put any expression into I or n or m and so on. Best