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MathGroup Archive 2007

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Re: LegendreP error (bug?) in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81140] Re: LegendreP error (bug?) in Mathematica
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 14 Sep 2007 03:27:38 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • 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. 

<snip>

Seems to work like a charm with Mathematica 6.0.1. See

http://homepages.nyu.edu/~jmg336/mathematica/LegendreP601.pdf

-- 
Jean-Marc


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