(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Obtain the recurrene relation between the coefficient a_{r}in the series solution

y= (between r=0 and [tex]\infty[/tex]) [tex]\Sigma[/tex] a_{r}x^{r}

to (1-x^{2})y''-2xy'+k(k+1)y=0

Deduce that if k is a positive integer, then a_{k+2}=0, so that the equation possesses a solution which is a polynomial of degree k.

2. Relevant equations

(there is more to this question....but i think ill try getting through this bit first!)

3. The attempt at a solution

I have managed to get the correct recurrance relation

(n+2)(n+1)a_{n+2}-a_{n}(n(n+1)-k(k+1))=0

But i have no idea what to do now (the show if k is a positive integer) etc :-(

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# Homework Help: Legendre's equation

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