Convergence of lattice sums and Madelung’s constant

DOI10.1063/1.526675zbMath0587.40007OpenAlexW2032372625WikidataQ56658203 ScholiaQ56658203MaRDI QIDQ3712872

Keith F. Taylor, Jonathan M. Borwein, David Borwein

Publication date: 1985

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1959.13/1043576

zbMATH Keywords

Mellin transformtheta functionlattice sumshexagonal latticeintegral transformation methodsdirect sum methodsMadelung's constantNaCl-type crystal lattice

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Multiple sequences and series (40B05)

Related Items (15)

Coulomb and Riesz gases: The known and the unknown ⋮ Determination of some lattice sum limits ⋮ Born-Infeld particles and Dirichlet \(p\)-branes ⋮ Periodic discrete energy for long-range potentials ⋮ Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi ⋮ Flexibly imposing periodicity in kernel independent FMM: a multipole-to-local operator approach ⋮ Convergence analysis of the Wolf method for Coulombic interactions ⋮ FromL-series of elliptic curves to Mahler measures ⋮ Corner ion, edge-center ion, and face-center ion madelung expressions for sodium chloride ⋮ New Representations for the Madelung Constant ⋮ One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation ⋮ Analytical methods for fast converging lattice sums for cubic and hexagonal close-packed structures ⋮ The Charge-Group Summation Method for Electrostatics of Periodic Crystals ⋮ Convergence of Madelung-like lattice sums ⋮ The Electrostatic Potential of Periodic Crystals

Cites Work

• On the Stability of Certain Heteropolar Crystals
• Über die Konvergenz der Reihen Epsteinscher Zetafunktionen. Erhard Schmidt zum, 75. Geburtstag.

This page was built for publication: Convergence of lattice sums and Madelung’s constant