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