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
> 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,
>