Fast construction of Fejér and Clenshaw–Curtis rules for general weight functions

The main purpose of this paper is to compute the weights of Clenshaw–Curtis and Fejér type quadrature rules via DCT and DST, for general weight functions ww. The approach is different from that used by Waldvogel (2006) in [10], where the author considered the computation of these sets only for the Legendre weight w≡1w≡1 using DFT arguments.