A novel approach for the computation of orthonormal polynomial expansions

In this paper we present a novel technique for the computation of orthonormal polynomial expansions. The proposed method is very straightforward; given a function to be expanded in a polynomial series, we first use the FFT to compute a vector of Fourier coefficients. Then, using a change of basis transformation, we go from the Fourier coefficients to the polynomial coefficients. Convergence properties for this new approach are investigated.