On a quiz I was given the problem" a series that is a basis for $[-1,1]$ is $ \sum_0^{\infty} c_n P_n $, where $ P_n $ is a polynomial and each polynomial $P_n$ is orthonormal to the others. Using the dot product definition used in Fourier series, what is the formula for computing $c_5$?" I really have no idea.i believe we are supposed to use the wedge product? But I'm not sure how to use that. Maybe $\int_{-1}^1 \sum_0^{5} c_n P_n dx $? That is really the only thing I can think of but I don't know what to do with it or how to apply it. I believe the polynomial is called a legendre polynomial?
2026-04-11 16:49:46.1775926186
Issues proving a basis via wedge product
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