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 (?).