Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?)

share|improve this question
    
If it's a school assignment you should tag it as homework. What did google tell you about Legendre polynomials? –  draks ... Apr 22 '12 at 21:22
    
I guess my first question is more related to e. Is that just a variable? –  Special--k 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 1

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.

share|improve this answer
    
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. –  Special--k 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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.