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Math Help - Recurrence Relations for Laguerre Polynomials

  1. #1
    Member iPod's Avatar
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    Recurrence Relations for Laguerre Polynomials

    The Laguerre polynomials L_n(x) are given by the explicit formula

    L_n(x)=\sum_{m=0}^{n}(-1)^m\frac{n!}{(n-m)!(m!)^2}x^m

    Recall that the coefficients of the Laguerre polynomials can be calculated using the recurrence relation;

    a_{m+1}=\frac{m-n}{(m+1)^2}a_m ,  a_0=1

    For fixed n use induction to prove the above summation formula.

    I'm not too sure how to approach this question whether its through dummy variables or telescopic sums or whatever.
    Help would be much be appreciated. Thank you
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  2. #2
    Grand Panjandrum
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    Re: Recurrence Relations for Laguerre Polynomials

    Quote Originally Posted by iPod View Post
    The Laguerre polynomials L_n(x) are given by the explicit formula

    L_n(x)=\sum_{m=0}^{n}(-1)^m\frac{n!}{(n-m)!(m!)^2}x^m

    Recall that the coefficients of the Laguerre polynomials can be calculated using the recurrence relation;

    a_{m+1}=\frac{m-n}{(m+1)^2}a_m ,  a_0=1

    For fixed n use induction to prove the above summation formula.

    I'm not too sure how to approach this question whether its through dummy variables or telescopic sums or whatever.
    Help would be much be appreciated. Thank you
    Use induction.

    CB
    Last edited by CaptainBlack; November 25th 2011 at 11:59 AM.
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