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MathGroup Archive 2007

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Re: LegendreP error (bug?) in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81178] Re: LegendreP error (bug?) in Mathematica
  • From: roland franzius <roland.franzius at uos.de>
  • Date: Fri, 14 Sep 2007 03:47:24 -0400 (EDT)
  • Organization: Universitaet Hannover
  • References: <fcb3qh$fk1$1@smc.vnet.net>

John Ralston wrote:
> LegendreP[ l, m] and SphericalHarmonicY[ t, p, l, m]  go
> wrong for large index l .  
> 
> For l> 40 or so neither can be used reliably everywhere. 
> 
> To see the breakdown plot the functions.  Not all index cases fail.
> Here's some examples: 
> 
> Plot[LegendreP[ 44, 13, x] , {x, -1, 1} ]
> 
> Plot[LegendreP[ 66, 9, x] , {x, -1, 1} ]
> 
> ListPlot[ Table[ {j,
>      Sqrt[ 4Pi/ (
>       2l + 1) ] Abs[ SphericalHarmonicY[ j, 0, 0,
>                      3.7 ]]}, {j, 1, 55}], PlotJoined -> True]
> 
> Has anyone fixed this?  Does anyone care? 
> I need l ranges above 200. 
> 
> thanks
> John Ralston 
> 
> 
> 
>>I find serious bugs in Mathematica 5.1 LegendreP
>>and SphericalHarmonicY.  It is not a matter of 
>>definitions or syntax, but a catastrophic failure
>>easy to establish.  Math archives show a history
>>of discussion, but invariably centered on variations
>>of definition.
>>
>>
>>Wolfram Research shows little interest.  I'm
>>wondering if the failure
>>to perfom is well known and has been repaired by
>>someone 
>>re-writing the commands.  I don't often follow this
>>forum, but I've joined to either get access to code
>>that works, or to inform people so they can go after
>>the problem.   Does anyone care? 

Plotting of fast oscillating functions is incorrect if you don't 
prescibe number of PlotPoints.

Try about half the number of zeros

Plot[LegendreP[ 44, 13, x] , {x, -1, 1}, PlotPoints->25 ]

-- 

Roland Franzius


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