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Convergance of Madelung-like lattice sums

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posted on 2025-05-08, 14:22 authored by David Borwein, Jonathan M. Borwein, Christopher Pinner
We make a general study of the convergence properties of lattice sums, involving potentials, of the form occurring in mathematical chemistry and physics. Many specific examples are studied in detail. The prototype is Madelung's constant for NaCl: [formula could not be replicated]= -1.74756459···, presuming that one appropriately interprets the summation proccess.

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  1. 1.
    DOI - Is published in https://doi.org/10.1090/S0002-9947-98-01983-7
  2. 2.
    ISSN - Is version of https://portal.issn.org/resource/ISSN/0002-9947

Journal title

Transactions of the American Mathematical Society

Volume

350

Issue

8

Pagination

3131-3167

Publisher

American Mathematical Society (AMS)

Language

  • en, English

College/Research Centre

Faculty of Science and Information Technology

School

School of Mathematical and Physical Sciences

Rights statement

First published in Transactions of the American Mathematical Society in Vol. 350, No.8, pp. 3131-3167, 1998, published by the American Mathematical Society.

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    Keywords

    lattice sumszeta functionsconditional convergenceMadelung's constantDirichlet seriestheta functions

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