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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



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