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Re: SphericalHarmonics strange behavior

• To: mathgroup at smc.vnet.net
• Subject: [mg100982] Re: SphericalHarmonics strange behavior
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 19 Jun 2009 20:45:45 -0400 (EDT)
• Organization: Uni Leipzig
• References: <h1en59$i5n$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de

Hi,

there is *no* sign error. Mathematica don't know that
your polar angle can only take values 0<=th1<=Pi and

diffY[1, 1, th1, ph1] // FullSimplify[#, 0 <= th1 <= Pi] &

work as expected.

Regards
   Jens

lbloy at seas.upenn.edu wrote:
> Hi all,
> 
> working with some spherical harmonics and have some questions about the code as implemented in mathematica.
> 
> based on http://mathworld.wolfram.com/SphericalHarmonic.html
> 
> I put together the following code to see what is implemented
> 
> th1 = 1.324;
> ph1 = 5.231;
> 
> diffY[l_, m_, t_, p_] := 
>   Module[{val1, val2}, val1 = SphericalHarmonicY[l, m, t, p]; 
>         val2 = 
>     Sqrt[((2*l + 1)*(l - m)!)/((4*Pi)*(l + m)!)]*
>      LegendreP[l, m, Cos[t]]*E^(I*m*p); 
>         Print[{val1, val2, Abs[val1 - val2]}]; 
>    Return[Abs[val1 - val2]]; ]; 
> 
> diffY[1, 1, th1, ph1]
> 
> diffY[1, -1, th1, ph1]
> 
> Clearly there is some sign error somewhere I was wondering if anyone had any suggestions.
> 
> thanks
> Luke
>