My task is to find three orthogonal polynomials $P_0$, $P_1$ and $P_2$ under the dot product $<f, g> = f(-2)g(-2) + f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2)$.
I thought I could start with $P_0(x) = 1$, $P_1(x) = x$, $P_2(x) = x^2$ and then use the Gram-Schimdt orthogonalization process using the dot product defined above. Is this correct, and the easiest way of doing this?