Published June 9, 2017
| Submitted
Journal Article
Open
Integration by differentiation: new proofs, methods and examples
- Creators
- Jia, Ding
- Tang, Eugene
- Kempf, Achim
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.
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.Attached Files
Submitted - 1610.09702.pdf
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Additional details
- Eprint ID
- 77406
- DOI
- 10.1088/1751-8121/aa6f32
- Resolver ID
- CaltechAUTHORS:20170512-104125211
- National Science and Engineering Research Council of Canada (NSERC)
- Created
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2017-05-12Created from EPrint's datestamp field
- Updated
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2022-07-12Created from EPrint's last_modified field