Re: LegendreP error (bug?) in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg81126] Re: LegendreP error (bug?) in Mathematica
- From: John Ralston <ralston at ku.edu>
- Date: Thu, 13 Sep 2007 06:28:11 -0400 (EDT)
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
>