Keeping the Legendre polynomials in expressions without finding the explicit polinomials

*To*: mathgroup at smc.vnet.net*Subject*: [mg57798] Keeping the Legendre polynomials in expressions without finding the explicit polinomials*From*: "Vladislav" <kazimir04 at yahoo.co.uk>*Date*: Thu, 9 Jun 2005 05:17:32 -0400 (EDT)*References*: <d7dp2r$qam$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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