Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegö type, II

摘要

Generalizing the work of Gautschi and Notaris (1989), we consider Gauss-Kronrod quadrature formulae relative to weight functions on [-1, 1], consisting of any one of the four Chebyshev weight functions divided by a polynomial of arbitrary degree which remains positive on [-1, 1]. We show that beyond a certain n (the number of Gauss nodes), which depends on the weight function, the interlacing, inclusion and positivity properties hold. The precise degree of exactness for each of the quadrature formulae is also determined.