Legendre polynomials

  • Thread starter blueyellow
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  • #1
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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
 

Answers and Replies

  • #2
vela
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Let's clean up your notation a bit. You're given three of the Legendre polynomials:

[tex]\begin{align*}
P_0(x) &= 1 \\
P_1(x) &= x \\
P_2(x) &= (3x^2-1)/2
\end{align*}[/tex]

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

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

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