Integral over Spher. Harmon.

*To*: mathgroup at smc.vnet.net*Subject*: [mg4936] Integral over Spher. Harmon.*From*: "w.meeussen" <w.meeussen.vdmcc at vandemoortele.be>*Date*: Mon, 7 Oct 1996 02:02:09 -0400*Sender*: owner-wri-mathgroup at wolfram.com

to those having Mma 3.0 : how does Integrate[SphericalHarmonicY[l,m,th,fi]Sin[th],{th,0,Pi},{fi,0,2Pi}] evaluate for unspecified l and m ? does it bounce back the input, like in version 2.3.3 ? or does it give the proper : If[l==0&&m==0, 2 Sqrt[Pi], 0]? Check that, in version 2.3.3 , even explicitely limiting l and m to integers : Integrate[SphericalHarmonicY[l_Integer,m_Integer,th,fi]Sin[th],{th,0,Pi},{fi ,0,2Pi}] does not produce those results. Neither does : Integrate[SphericalHarmonicY[l_/;IntegerQ[l],m_/;IntegerQ[m],th,fi]Sin[th],{ th,0,Pi},{fi,0,2Pi}] Alternative question : is it easier in Mma 3.0 to "lock" a variable to integer, positive, real, etc.. domains ? In other words, does Sin[2 n_Integer Pi] evaluate to zero ? In previous questions & answer sessions (here and elsewhere), it was said that "locking" variables in such way is dangerous, undesirable , and leads to errors. Possible, but function definitions and variable assignments using "Set" are just as dangerous. Since they show up nicely using "?symbol", I see no danger. It feels as though a means of user control is withheld by not allowing "locking". How does Mma 3.0 react in this respect ? Wouter. ==== [MESSAGE SEPARATOR] ====