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MathGroup Archive 1996

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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.



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