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MathGroup Archive 2007

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Re: LegendreP error (bug?) in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81183] Re: LegendreP error (bug?) in Mathematica
  • From: Roman <rschmied at gmail.com>
  • Date: Fri, 14 Sep 2007 03:49:58 -0400 (EDT)
  • References: <fcb3qh$fk1$1@smc.vnet.net>

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.



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