How to define a specific definite integral result in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg125410] How to define a specific definite integral result in Mathematica*From*: Antonio Alvaro Ranha Neves <aneves at gmail.com>*Date*: Tue, 13 Mar 2012 03:02:00 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

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