Chebyshev-type quadrature formulas for new weight classes

Abstract

We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for applications. One of our motivations to consider these type of problems is the Faraday cage phenomenon for discrete charges as discussed by J. Korevaar and his colleagues.