Amer
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Let \{ \phi_0,\phi_1,...,\phi_n\} othogonal set of polynomials on [a,b] n>0, with a weight function w(x) prove that
\int_{a}^b w(x)\phi_n Q_k (x) \; dx = 0
for any polynomail Q_k(x) of degree k<n ?
My work :
I think there is a problem in the question since if we take x^2,x^3 on the interval [-1,1] they are orthogonal
but if we take x
\int_{-1}^{1} x(x^3 ) \; dx \neq 0
\int_{a}^b w(x)\phi_n Q_k (x) \; dx = 0
for any polynomail Q_k(x) of degree k<n ?
My work :
I think there is a problem in the question since if we take x^2,x^3 on the interval [-1,1] they are orthogonal
but if we take x
\int_{-1}^{1} x(x^3 ) \; dx \neq 0
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