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Math Help - legendre's polynomial...

  1. #1
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    legendre's polynomial...

    ok i have a problem, that im having trouble getting started...

    im supposed to use rodrigues formula, to find the Legendre's polynomials $P_{6}, P_{7} \and P_{8}.$


    P_{n}(x)=\frac{1}{2^{n}n!}\frac{d^{n}}{dx^{n}}(x^{  2}-1)^{n} <---would I just plug into the equation for n=0,1,2,3,...
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  2. #2
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by slapmaxwell1 View Post
    ok i have a problem, that im having trouble getting started...

    im supposed to use rodrigues formula, to find the Legendre's polynomials $P_{6}, P_{7} \and P_{8}.$


    P_{n}(x)=\frac{1}{2^{n}n!}\frac{d^{n}}{dx^{n}}(x^{  2}-1)^{n} <---would I just plug into the equation for n=0,1,2,3,...
    The Rodriguez formula requires the computation of high order derivatives. An confortable alternative approach is the use of the recursive relation...

    \displaystyle P_{n+1} (x) = \frac{2n+1}{n+1}\ x\ P_{n} (x) - \frac{n}{n+1}\ P_{n-1} (x) (1)

    ... starting from P_{0}(x)=1 and P_{1}(x)=x...

    Kind regards

    \chi \sigma
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