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MathGroup Archive 2007

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Re: Integrating SphericalHarmonicY

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73208] Re: Integrating SphericalHarmonicY
  • From: "Roman" <rschmied at gmail.com>
  • Date: Wed, 7 Feb 2007 06:02:43 -0500 (EST)
  • References: <eq9c4v$n37$1@smc.vnet.net>

What you say is only (?) true if l is an integer >= 0 and m is an
integer -l <= m <= l, or if l is a half-integer >=0 and m is a half-
integer -l <= m <= l. But in general, the integral you give does not
converge. As the manual for Integrate says,

> For indefinite integrals, Integrate tries to find results that are correct for almost all values of parameters.

And since what you say is wrong for almost all values of l and m, it
tells you so.

If you tell us what the circumstances are, in which you need this
simplification, maybe we can help you more.

Roman.

On Feb 6, 8:53 am, wgem... 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.




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