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Orthogonalize { 1, t, t2 } in P2 (R) with (f,g) = f(x)g(x) dx. Then normalize each one so that its graph passes through (1,

Orthogonalize { 1, t, t2 } in P2 (R) with (f,g) = f(x)g(x) dx. Then normalize each one so that its graph passes through (1, 1). These are the first three Legendre polynomials. Check

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