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

```

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