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