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MathGroup Archive 2006

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Re: Problem plotting high-order Laguerre polynomials

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64211] Re: Problem plotting high-order Laguerre polynomials
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Mon, 6 Feb 2006 02:49:11 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <dqn7br$l3v$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <dqn7br$l3v$1 at smc.vnet.net>,
 "Elinor K. Irish" <eirish at pas.rochester.edu> wrote:

> I'm doing some work which involves plotting fairly high-order Laguerre
> polynomials, up to 200 or so.  I've been getting some very strange and
> obviously incorrect results which seem to have to do with the order of
> evaluation.  (I'm using Mathematica 5.0, but I've checked it in 5.2 and I
> get the same problems.)  Here are some examples with a simple form of the
> type of function I'm working with:
> 
> func = 1/Pi Exp[- q^2] LaguerreL[n, 2 q^2]

Another approach to plotting/computing high-order polynomials is to use 
an appropriate asymptotic form. Note that (from Szego or Abramowitz and 
Stegun) the leading term in the asymptotic expansion for large n is

  Exp[- x/2] LaguerreL[n, x] ~ BesselJ[0, 2 Sqrt[n x]]

See also http://locus.siam.org/SIMA/volume-19/art_0519087.html.

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    
AUSTRALIA                               http://physics.uwa.edu.au/~paul


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