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MathGroup Archive 2005

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Re: Keeping the Legendre polynomials in expressions without finding the explicit polinomials

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57833] Re: Keeping the Legendre polynomials in expressions without finding the explicit polinomials
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 9 Jun 2005 05:55:34 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <d7dp2r$qam$1@smc.vnet.net> <d891no$s42$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

insert a new symbol say LPolynom[n,x] and if you 
need the
explicit form say LPolynom -> LengendreP
poly = LPolynom[5, x] + LPolynom[6, x]/4

poly /. LPolynom -> LegendreP

Regards

  Jens



"Vladislav" <kazimir04 at yahoo.co.uk> schrieb im 
Newsbeitrag news:d891no$s42$1 at smc.vnet.net...
> Hi, all,
>
> Thank you for your replies. I have learnt a lot 
> of usefull things, but
> Infortunately I had simplified my task very 
> much, so that I could not
> apply any answer directly to my case.
>
> Can somebody help me with the following. I need 
> present some functions
> (prolate spheroidal functions) in the basis of 
> the Legendre
> polynomials. I.e. I have functions like
>
> FF1 = 0.6 LegendreP[5, #1] + 0.7 LegendreP[6, 
> #1] &
> FF2 = 0.3 LegendreP[5, #1] + 0.2 LegendreP[6, 
> #1] &
>
> I want to manipulate these functions and remain 
> in the basis of prolate
> functions.  For example I want to create a 
> linear combination of
> functions, or something like this.
>
> FF = .2FF1[#1] + .3FF2[#1] &
>
> It works well from the point of view of finding 
> the numerical result,
> but it do not give the presentaion of the 
> function in the basis of the
> Legendre polynomials.
>
> I would like to have create a function which 
> would give the result like
>
> FFX = 0.9 LegendreP[5, #1] + 0.9 LegendreP[6, 
> #1] &,
> so that I could see the presentaion of the 
> function by typing FFX and
> obtaining  0.9 LegendreP[5, #1] + 0.9 
> LegendreP[6, #1] &. In practice
> these functions contain much more terms and 
> having the form like  0.9
> LegendreP[5, #1] + 0.9 LegendreP[6, #1] & is 
> very important. At the
> same time I would not like to have the explicit 
> presentation as
> plolinomials, like -0.28125+1.6875  w + 5.90625 
> w^2 + .. because of
> loss of accuracy for future results.
>
> Sincerely,
>
> Vlad
> 



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