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Re: Laguueree polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg24001] Re: Laguueree polynomials
• From: "A. E. Siegman" <siegman at stanford.edu>
• Date: Mon, 19 Jun 2000 01:45:44 -0400 (EDT)
• Organization: Stanford University
• References: <8ihus7$lds@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <8ihus7$lds at smc.vnet.net>, Wissam Alsaidi 
<alsaidi at pacific.mps.ohio-state.edu> wrote:

> Hi all,
> 
> I have done some calculation in mathematica which involves adding and
> plotting like thousand of Laguueree polynomials with n between 0 and 5 and
> the angular index which is as big as 500.These polynomials are highly
> oscillatory functions.I did nor recieve any error message  through out the
> calculation.My question is to what extent I can trust the graph I am
> getting.In fact I suspect that the result is true form physical arguments
> so can I trust the mathematica part of the calulation and look for another
> source of error. 
> 
> Thanks  in advance.
> Wissam
> 
> 

Can't answer your direct question, but I have done expansions using very 
high *order* Hermite or Laguerre polynomials with moderately large 
arguments and found that I got much better accuracy if the arguments 
were totally integer in character, e.g. f[1001/1000] was much more 
accurate (at large orders) than f[1.001] -- presumably because the first 
case expands the polynomial using purely integer arithmetic (?).