Quadrature sums and Lagrange interpolation for general exponential weights (Q1872992)

This paper is concerned with the derivation of forward and converse quadrature sum estimates associated with zeros of an orthogonal polynomials for general exponential weights \(W(x)\) such that \[ W(x)=\exp(-(1-x^2)^ {-\alpha }), \quad x\in \mathbb R, \quad \alpha >0. \] The application to the mean convergence of Lagrange interpolation at zeros of orthogonal polynomial, that has been throughly investigated for even exponential weights, is here extended by considering noneven weights on a real interval \(I=(c,d)\), where \(-\infty \leq c < 0 < d \leq \infty .\)