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 >