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. >