Expanding 6x^2 in Terms of Legendre Polynomials

[blueyellow]

Given the Legendre polynomials P0(x) = 1, P1(x) = x and P2(x) = (3x2
−
1)/2, expand the polynomial 6(x squared) in terms of P l (x).

does anyone know what this question is asking me? what is P l (x)?
thanks in advance

 

[vela]

Let's clean up your notation a bit. You're given three of the Legendre polynomials:

\begin{align*}<br /> P_0(x) &amp;= 1 \\<br /> P_1(x) &amp;= x \\<br /> P_2(x) &amp;= (3x^2-1)/2<br /> \end{align*}

The problem is asking you to expand the polynomial 6x^2 in terms of these polynomials. In other words, you want to find constants c₀, c₁, and c₂ such that

6x^2 = c_0 P_0(x) + c_1 P_1(x) + c_2 P_2(x)[/tex]