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