Maximal generalization of Lanczos' derivative using one-dimensional integrals

TL;DR

This paper presents a maximal generalization of the differentiation by integration method using one-dimensional integrals, including new non-analytic weight functions, to improve the derivative approximation process.

Contribution

It introduces a broad generalization of existing integral-based derivative formulas, expanding the class of weight functions and enhancing the method's flexibility.

Findings

Provides a maximal generalization of Lanczos' derivative formula

Introduces new non-analytic weight functions for differentiation

Enhances the theoretical framework for integral-based derivatives

Abstract

Derivative of a function can be expressed in terms of integration over a small neighborhood of the point of differentiation, so-called differentiation by integration method. In this text a maximal generalization of existing results which use one-dimensional integrals is presented together with some interesting non-analytic weight functions.