Integration by differentiation: new proofs, methods and examples. (11th May 2017)

• Record Type: Journal Article
• Authors: Jia, Ding; Tang, Eugene; Kempf, Achim
• Is Part Of: Journal of physics. Volume 50:Number 23(2017)
• Publication Date: 2017-05-11
• Subjects: integration -- differentiation -- Fourier transform -- Laplace transform -- Dirac delta -- Borwein integral -- quantum field theory; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa6f32
• Languages: English
• ISSNs: 1751-8113

Abstract

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.