Sasane, Amol (2020) A summation method based on the Fourier series of periodic distributions and an example arising in the Casimir effect. Indagationes Mathematicae, 31 (3). 477 - 504. ISSN 0019-3577
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Text (A summation method based on the Fourier series of periodic distributions and an example arising in the Casimir effect)
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Abstract
A generalised summation method is considered based on the Fourier series of periodic distributions. It is shown that [Formula presented], where [Formula presented] is the 2π-periodic distribution given by [Formula presented] for φ∈D(R) with support supp(φ)⊂(−δ,2π+δ), where δ∈(0,π). Applying the generalised summation method, the sum of the divergent series 1+2+3+⋯ (arising in a quantum field theory calculation in the Casimir effect) is determined, and more generally also the sum 1 k+2 k+3 k+⋯, for k∈N, is determined.
Item Type: | Article |
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Official URL: | https://www.sciencedirect.com/journal/indagationes... |
Additional Information: | © 2020 Royal Dutch Mathematical Society |
Divisions: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Date Deposited: | 24 Mar 2020 14:18 |
Last Modified: | 20 Jun 2024 21:30 |
URI: | http://eprints.lse.ac.uk/id/eprint/103822 |
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