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MathGroup Archive 2007

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Re: LegendreP Evaluation Mystery

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75155] Re: LegendreP Evaluation Mystery
  • From: AES <siegman at stanford.edu>
  • Date: Wed, 18 Apr 2007 05:12:07 -0400 (EDT)
  • Organization: Stanford University
  • References: <evvaqs$95r$1@smc.vnet.net>

In article <evvaqs$95r$1 at smc.vnet.net>, "Antonio" <aneves at gmail.com> 
wrote:

> And it is worse for m=0. Does Mathematica evaluate LegendreP
> differently for high n's, why does it take so long? Is there any way

Don't know if this will  be of any help, but some years ago I was 
evaluating numerical values of Legendre polynomials for high n (in the 
50s to 60s) and encountered round-off errors (or what looked like 
round-off errors any way) with real arguments, that disappeared when I 
used rational integer or exact arguments.

Example:  I wanted to vary the argument by very small steps around Pi.  
Using Pi, 1.001 Pi, 1.002 Pi, etc gave an obviously noisy sequence of 
values.  Using Pi, (1001 Pi/1000), (1002 Pi/1000) gave a much smoother 
sequence.  I assumed it had something to do with this being a 
polynomial, and Mathematica switching to some kind of integer arithmetic (???).


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