Linear Algebra and Its Applications · Problem 3.4.24

Orthogonality — Gilbert Strang

Mathematics · legendre-polynomials

Problem

Find the fourth Legendre polynomial. It is a cubic

x^3 + ax^2 + bx + c

that is orthogonal to

1

x

, and

x^2 - \frac{1}{3}

over the interval

-1 \leq x \leq 1