On expansions in orthogonal polynomials (Q1946476)

In 2011, \textit{A. Iserles} [Numer. Math. 117, No. 3, 529--553 (2011; Zbl 1211.33001)] introduced an \(\mathcal{O}(N \log N)\) algorithm for the computation of the first \(N\) coefficients in an expansion of an analytic function in Legendre polynomials. The same year, the authors extended the underlying framework to expansions in ultraspherical polynomials. These approaches rest upon three steps. In the paper under review, the authors demonstrate that the first two steps remain valid for a large variety of orthogonal systems.