Uniform convergence of derivatives of extended Lagrange interpolation

Summary The authors construct some extended interpolation formulae to approximate the derivatives of a function in uniform norm. They prove theorems on uniform convergence and give estimates of pointwise type and of simultaneous approximation.This material is based upon work supported by the Italian Research Council (first and second authors), and by the Ministero dell'Università e della Ricerca Scientifica e Tecnologica (second and third author).