Re: Integrating SphericalHarmonicY
- To: mathgroup at smc.vnet.net
- Subject: [mg73199] Re: Integrating SphericalHarmonicY
- From: dh <dh at metrohm.ch>
- Date: Wed, 7 Feb 2007 05:26:20 -0500 (EST)
- References: <eq9c4v$n37$1@smc.vnet.net>
Hi,
if you want to define a rule for this integral for symbolic l and m, you
may define an Upvalue for e.g. Integrate:
Unprotect[Integrate]
Integrate[Conjugate[SphericalHarmonicY[l_, m_, theta_, phi_]]
SphericalHarmonicY[l_, m_, theta_, phi_] Sin[theta_], {theta_, 0, Pi},
{phi, 0, 2 Pi}] = 1
from now on this integral evaluates to 1.
Daniel
wgempel at yahoo.com wrote:
> I would like
>
> Integrate[
> Conjugate[SphericalHarmonicY[l,m,theta,phi]]
> SphericalHarmonicY[l,m,theta,phi] Sin[theta],
> {theta, 0, Pi}, {phi, 0, 2 Pi}]
>
> to evaluate to 1 (without having to force it through a rule every
> time).
>
> I have tried
> $Assumptions =
> {Element[Alternatives[theta,phi], Reals] &&
> Element[Alternatives[l,m], Integers] &&
> l >= Abs[m]}
>
> Thanks for any help.
>