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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 into Lánczos's derivative and its generalizations for n-th order derivatives. By the way, it says that the Lánczos's (1956) derivative formula goes back to Cioranescu (1938) and Haslam-Jones (1953).

In addition to J.M. answer: this paper https://www.sciencedirect.com/science/article/pii/S0021904512000123 (Differentiation by integration using orthogonal polynomials, a survey, by E. Diekema and T.H. Koornwinder, doi: 10.1016/j.jat.2012.01.003) provides further insight into Lánczos's derivative and its generalizations for n-th order derivatives. By the way, it says that the Lánczos's (1956) derivative formula goes back to Cioranescu (1938) and Haslam-Jones (1953).

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 into Lanczo's derivative and its generalizations for n-th order derivatives. By the way, it says that the Lanczo's(1956) derivative formula goes back to Cioranescu(1938) and Haslam-Jones(1953).

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 into Lánczos's derivative and its generalizations for n-th order derivatives. By the way, it says that the Lánczos's (1956) derivative formula goes back to Cioranescu  (1938) and Haslam-Jones  (1953).

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).

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 into Lanczo's derivative and its generalizations for n-th order derivatives. By the way, it says that the Lanczo's(1956) derivative formula goes back to Cioranescu(1938) and Haslam-Jones(1953).