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Integration by differentiation: new proofs, methods and examples

Jia, Ding and Tang, Eugene and Kempf, Achim (2017) Integration by differentiation: new proofs, methods and examples. Journal of Physics A: Mathematical and Theoretical, 50 (23). Art. No. 235201. ISSN 1751-8113. doi:10.1088/1751-8121/aa6f32.

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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.

Item Type:Article
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Additional Information:© 2017 IOP Publishing Ltd. Received 30 October 2016. Accepted 25 April 2017. Accepted Manuscript online 25 April 2017. Published 11 May 2017. AK acknowledges support through the Discovery Program of the National Science and Engineering Research Council (NSERC) of Canada. DJ acknowledges useful discussions with Yidong Chen.
Funding AgencyGrant Number
National Science and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Subject Keywords:integration, differentiation, Fourier transform, Laplace transform, Dirac delta, Borwein integral, quantum field theory
Issue or Number:23
Record Number:CaltechAUTHORS:20170512-104125211
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Official Citation:Ding Jia et al 2017 J. Phys. A: Math. Theor. 50 235201
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77406
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 22:22
Last Modified:12 Jul 2022 19:46

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