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MathGroup Archive 2007

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Re: Re: LegendreP error (bug?) in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81171] Re: [mg81126] Re: LegendreP error (bug?) in Mathematica
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 14 Sep 2007 03:43:46 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

In version 6 I do not see a problem with the first two examples. In the third example, l is undefined. Defining l and changing 3.7 to 37/10 (use rational numbers to maintain high precision) works fine. Alternatively, specify higher precision (e.g., 3.7`25). Also, in version 6, Plot has an option to change (increase) the WorkingPrecision.


Bob Hanlon

---- John Ralston <ralston at ku.edu> 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? 
> > 
> > John Ralston
> >
> 



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