Orthogonal polynomials, Legendre

We note that we have three equations to determine the three coefficients $a$, $b$ and $c$.

Alternatively, we could have employed the recursion relation of Eq. (11), resulting in $$\begin{equation*} 2L_2(x)=3xL_1(x)-L_0, \end{equation*}$$ which leads to Eq. (12).

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