A summation method based on the Fourier series of periodic distributions and an example arising in the Casimir effect

Sasane, Amol ORCID: 0000-0001-5566-9877 (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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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
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:	12 Dec 2024 02:05
URI:	http://eprints.lse.ac.uk/id/eprint/103822

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