Integration by differentiation: new proofs, methods and examples
Mathematical Physics
2017-06-02 v2 math.MP
Abstract
Recently, new methods were introduced which allow one to solve ordinary integrals by performing only derivatives. These studies were originally motivated by the difficulties of the quantum field theoretic path integral, and correspondingly, the results were derived by heuristic methods. Here, we give rigorous proofs for the methods to hold on fully specified function spaces. We then illustrate the efficacy of the new methods by applying them to the study of the surprising behavior of so-called Borwein integrals.
Keywords
Cite
@article{arxiv.1610.09702,
title = {Integration by differentiation: new proofs, methods and examples},
author = {Ding Jia and Eugene Tang and Achim Kempf},
journal= {arXiv preprint arXiv:1610.09702},
year = {2017}
}
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