The Madelung constant in N dimensions

Simple item page
dc.citation.issue2267
dc.citation.volume478
dc.contributor.authorBurrows A
dc.contributor.authorCooper S
dc.contributor.authorSchwerdtfeger P
dc.date.accessioned2023-11-12T22:15:38Z
dc.date.accessioned2023-11-20T01:38:18Z
dc.date.available2022-11-16
dc.date.available2023-11-12T22:15:38Z
dc.date.available2023-11-20T01:38:18Z
dc.date.issued2022-11-30
dc.description.abstractWe introduce two convergent series expansions (direct and recursive) in terms of Bessel functions and the number of representations of an integer as a sum of squares for N-dimensional Madelung constants, MN(s), where s is the exponent of the Madelung series (usually chosen as s=1/2). The convergence of the Bessel function expansion is discussed in detail. Values for MN(s) for s=1/2,3/2,3 and 6 for dimension up to N=20 are presented. This work extends Zucker's original analysis on N-dimensional Madelung constants for even dimensions up to N=8.
dc.description.confidentialfalse
dc.edition.editionNovember 2022
dc.identifier.citationBurrows A, Cooper S, Schwerdtfeger P. (2022). The Madelung constant in N dimensions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 478. 2267.
dc.identifier.doi10.1098/rspa.2022.0334
dc.identifier.eissn1471-2946
dc.identifier.elements-typejournal-article
dc.identifier.issn1364-5021
dc.identifier.number20220334
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/69174
dc.languageEnglish
dc.publisherRoyal Society
dc.publisher.urihttps://royalsocietypublishing.org/doi/10.1098/rspa.2022.0334
dc.relation.isPartOfProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
dc.rights(c) The author/s CC BY 4.0en
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subjectMadelung constant
dc.subjectlattice sums,
dc.subjectNdimensions
dc.titleThe Madelung constant in N dimensions
dc.typeJournal article
pubs.elements-id458513
pubs.organisational-groupOther
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