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I am working on a school assignment so U understand if you all are reluctant to give exact answers, but U could really use some guidance. I have a few questions, and to keep things organized i will post only one per thread. This thread is regarding Legendre, here is the exact question as per my assignment:

 Legendre Polynomials i) Find the Legendre polynomial e8(x) of degree 8. ii) Evaluate e8(x) at x = −1.0, −0.9, −0.8, . . . , +1.0 to isolate each of the eight roots of e8 in an interval of length 0.1. iii) Apply Newton’s method to approximate the roots r8,1, . . . , r8,8 of e8 to within 10−50. Display the roots in a table in increasing order. iv) Approximate the coefficients c8,1, . . . , c8,8 to within 10−50 and display their values in a table. 

Im currently at a total loss on this questions. I dont even really know what e8 reefers too.

I am using MAPLE to write scripts to calculate these values, so i do not need to pen/paper it.

Edit: I have parts i, ii, iii done. Im not sure exactly what iv is asking me to do. (can i attach text files on here somehow?)

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    How can that be? I would guess it the $P_n$ from the Wiki page given by Ross.2012-04-22

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Did you look up Wikipedia? Part i is there. From there ii should not be too hard. For iii, there is an expression for the derivative-do you understand how to to Newton's method? I'm not sure what you mean by "r8,1, . . . , r8,8". You are right that there should be eight real roots. I also don't understand question iv. You have the coefficients of the polynomial in i.

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    @Special--k: in the question, e8 seems to be the name of the Legendre polynomial. So, yes this e8(x) seems to be the same as P_8(x). I'm not sure what to make of the $e$ in the title.2012-04-22