Consider the inner-product (f; 9) := [_*¸ ƒ(x)g(x)dx. Consider the 'vectors' in this function space {y₁ (x), Y2 (x), Y3(x)} = {1, x, x²}. Perform the G-S procedure to produce three orthonormal polynomials {q₁(x), 92(x), 93 (x)}; this will produce the first three Legendre polynomials.

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