# 8Th Legendre Polynomial of $e$

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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I guess my first question is more related to e. Is that just a variable? – KevinCameron1337 Apr 22 '12 at 21:37
How can that be? I would guess it the $P_n$ from the Wiki page given by Ross. – draks ... Apr 22 '12 at 21:40

## 1 Answer

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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for i then, you are thinking the e is just a variable and should be treated as x in the wiki example? Yes, i can do Newton's no problem. – KevinCameron1337 Apr 22 '12 at 21:35
@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. – Ross Millikan Apr 22 '12 at 21:38