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.