You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Differentiation by integration using orthogonal polynomials, a survey 
Chapter Title:  Lanczos' 1956 work 
1. Abstract of Cited Paper (BIB001):  The method of differentiation by integration due to Lanczos is generalized to cover derivatives of arbitrary order. Umbral versions and further extensions are indicated. 
2. Abstract of Cited Paper (BIB002):  Everyone knows that the derivative of a function at a point measures the slope, or instantaneous rate of change, of the function at that point; this follows from the usual difference-quotient definition. However, various alternate formulations of the derivative have proved valuable. Many of these are discussed in Bruckner's text [1]. The Lanczos derivative is one alternate definition not mentioned by Bruckner, which has been a focus of recent attention [3, 5, 10]. Attributed to the Hungarian-born mathematician Cornelius Lanczos (pronounced Lan'tsosh) [7], this derivative is actually defined in terms of a definite integral! The Lanczos derivative of a function f at x is given by

Literature Review:
In a book published in 1956 Lanczos [42, (5-9.1)], apparently unaware of the earlier work by Cioranescu  and Haslam-Jones  , rediscovered formula (3.7). He called this differentiation by integration. His work got quite a lot of citations, see for instance  ,  , BIB001 , BIB002 , BIB003 ,  ,  . The name Lanczos derivative, notated as f L (x), became common for a value obtained from the right-hand side of (3.7). In BIB002 and BIB003 also (3.6) (the Legendre case for general n) was rediscovered. As an important new aspect Lanczos observed that 3 2δ as an approximation of f (x), is the limit as N → ∞ of the quotient of Riemann sums We have seen this last expression already in (3.5) (the special case of (3.1) with a centered Gram polynomial of degree 1). The expression approximates f (x) for N −1 δ small. In fact, (3.5) was the starting point of Lanczos, see [42, (5-8.4) ].