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 > > >