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