Re: Re: LegendreP error (bug?) in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg81206] Re: [mg81183] Re: LegendreP error (bug?) in Mathematica
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 15 Sep 2007 04:17:03 -0400 (EDT)
- Reply-to: hanlonr at cox.net
This is a precision issue. Use greater precision or rationalize the argument . LegendreP[200, 43, 4/5] // N 2.9256424676613492*^97 LegendreP[200, 43, 0.8`50] 2.92564246766126564673216*10^97 Bob Hanlon ---- Roman <rschmied at gmail.com> wrote: > I confirm the problem. Just as an example, > > In[1] := LegendreP[200, 43, 4/5] // N > Out[1] = 2.9256424676613492`*^97 > > In[2] := LegendreP[200, 43, 0.8] > Out[2] = 6.151579920980095`*^118 > > give strikingly different results! (The former result is accurate.) > > It seems that this problem occurs only for the associated Legendre > polynomials with large m; for m=0 the numerical result is accurate. > MathWorld (http://mathworld.wolfram.com/LegendrePolynomial.html) gives > a recursion relation (Eq. 66) for the associated Legendre polynomials, > and I was under the impression that this gave stable results. John, > maybe you can use this recursion relation to get better results, or > you can call the GNU Scientific Library through MathLink (http:// > www.gnu.org/software/gsl/). Bhuvanesh, I am very curious how you > explain this behavior. > > Roman. > >