Re: Preventing LegendreP from self-extracting in manipulations

*To*: mathgroup at smc.vnet.net*Subject*: [mg57861] Re: Preventing LegendreP from self-extracting in manipulations*From*: David Bailey <dave at Remove_Thisdbailey.co.uk>*Date*: Fri, 10 Jun 2005 02:29:27 -0400 (EDT)*References*: <d893ok$svp$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Vladislav wrote: > 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 > Hi, You may find it useful to use some other function for the Legendre polynomials - say P[x,n] - and then you can manipulate expressions involving this quite freely because Mathematica does not know anything about them. When you want numerical answers, you can use something like expr /. P[a_,b_]->LegendreP[a,b] Using this technique, you could even apply an identity involving LegendreP to your expressions! David Bailey http://www.dbaileyconsultancy.co.uk