Preventing LegendreP from self-extracting in manipulations

*To*: mathgroup at smc.vnet.net*Subject*: [mg57829] Preventing LegendreP from self-extracting in manipulations*From*: "Vladislav" <kazimir04 at yahoo.co.uk>*Date*: Thu, 9 Jun 2005 05:55:30 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, all, I have already tried to post the message, but it went lost. I repeat it as a new therad. 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. In the same way 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, Vladislav