Approximation of weight function and approached Padé approximants

摘要

We discuss the orthogonal expansion of a distribution dψ whose support [−1, 1] and first N + 1 moments c0, c1,…,cN are given. The truncated orthogonal expansion dψN gives rise to approached orthogonal polynomials and so to approached Padé approximants of the Stieltjes function with the distribution dψ.