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