New interpolatory quadrature formulae with Chebyshev abscissae

We study interpolatory quadrature formulae, relative to the Legendre weight function on [−1,1], having as nodes the zeros of any one of the four Chebyshev polynomials of degree n plus one of the points 1 or −1. In particular, we derive explicit formulae for the weights and examine their positivity, we determine the precise degree of exactness, we obtain asymptotically optimal error bounds, and we examine the definiteness f these quadrature formulae. In addition, we establish their convergence for Riemann integrable functions on [−1, 1] as well as for functions having a monotonic singularity at −1 or 1.