In addition to J.M. answer: this paper http://www.sciencedirect.com/science/article/pii/S0021904512000123 (Differentiation by integration using orthogonal polynomials, a survey, by E. Diekema and T.H. Koornwinder) provides further insight to Lanczo's derivative and its generalizations for  nn-th order derivatives. By the they it says that the Lanczo's(1956) derivative formula goes back to Cioranescu(1938) and Haslam-Jones(1953).