Some results in the theory of interpolation using the Legendre polynomial and its derivative

Uniform convergence of derivatives of extended Lagrange interpolation

“…For some extended system of nodes we refer the reader to [7,8,9,10,11,28]. In the present paper we prove that, by a suitable choice of the number of additional points or of the exponents of the generalized Jacobi weight, the approximation of a function and its derivatives by the Lagrange interpolation is optimal.…”