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Original Articles

New Representations for the Madelung Constant

Pages 367-379 | Published online: 03 Apr 2012

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David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor & Eric W. Weisstein. (2006) Ten Problems in Experimental Mathematics. The American Mathematical Monthly 113:6, pages 481-509.
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Jonathan Borwein & Kwok-Kwong Stephen Choi. (2000) On the Representations of xy + yz + ZX. Experimental Mathematics 9:1, pages 153-158.
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Articles from other publishers (28)

Antony Burrows, Shaun Cooper & Peter Schwerdtfeger. (2023) Lattice sum for a hexagonal close-packed structure and its dependence on the ratio of the hexagonal cell parameters . Physical Review E 107:6.
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Ahmed Sebbar. 2023. Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis. Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis 305 343 .
Antony Burrows, Shaun Cooper & P. Schwerdtfeger. (2022) The Madelung constant in N dimensions . Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 478:2267.
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Ahmed Sebbar & Roger Gay. (2021) Arithmetic and Analysis of the Series $${ \sum _{n=1}^{\infty } \frac{1}{n} \sin \frac{x}{n} }$$. Complex Analysis and Operator Theory 15:3.
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Jeffrey Rauch & L. Ridgway Scott. (2021) The Electrostatic Potential of Periodic Crystals. SIAM Journal on Mathematical Analysis 53:2, pages 1474-1491.
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Bartosz Kohnke, Carsten Kutzner & Helmut Grubmüller. (2020) A GPU-Accelerated Fast Multipole Method for GROMACS: Performance and Accuracy. Journal of Chemical Theory and Computation 16:11, pages 6938-6949.
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Jan GyllenbokJan Gyllenbok. 2018. Encyclopaedia of Historical Metrology, Weights, and Measures. Encyclopaedia of Historical Metrology, Weights, and Measures 33 238 .
Eric T. Mortenson. (2017) A Kronecker-type identity and the representations of a number as a sum of three squares. Bulletin of the London Mathematical Society 49:5, pages 770-783.
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Malik Mamode. (2016) Computation of the Madelung constant for hypercubic crystal structures in any dimension. Journal of Mathematical Chemistry 55:3, pages 734-751.
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Elsa Moggia. (2016) Pseudolattice Theory of electrolyte solutions: Consistency analysis of the Quasi-Random Lattice model at infinite dilution. Fluid Phase Equilibria 427, pages 231-245.
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Ikuo Fukuda. (2013) Zero-multipole summation method for efficiently estimating electrostatic interactions in molecular system. The Journal of Chemical Physics 139:17.
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Bruce C. Berndt, George Lamb & Mathew Rogers. (2012) Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi. The Ramanujan Journal 29:1-3, pages 185-198.
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E K Abalo, K A Milton & L Kaplan. (2012) Scalar Casimir energies of tetrahedra and prisms. Journal of Physics A: Mathematical and Theoretical 45:42, pages 425401.
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Leslie Glasser. (2012) Solid-State Energetics and Electrostatics: Madelung Constants and Madelung Energies. Inorganic Chemistry 51:4, pages 2420-2424.
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Władysław NarkiewiczWładysław Narkiewicz. 2012. Rational Number Theory in the 20th Century. Rational Number Theory in the 20th Century 13 129 .
Taweetham Limpanuparb & Peter M. W. Gill. (2011) Resolutions of the Coulomb Operator: V. The Long-Range Ewald Operator. Journal of Chemical Theory and Computation 7:8, pages 2353-2357.
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A. David Baker, Mark D. Baker & Christopher R. H. Hanusa. (2011) Corner ion, edge-center ion, and face-center ion Madelung expressions for sodium chloride. Journal of Mathematical Chemistry 49:6, pages 1192-1198.
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M. Rogers. (2010) Hypergeometric Formulas for Lattice Sums and Mahler Measures. International Mathematics Research Notices.
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C. M. Linton. (2010) Lattice Sums for the Helmholtz Equation. SIAM Review 52:4, pages 630-674.
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Shigeru Kanemitsu & Haruo Tsukada. 2010. The Legacy of Alladi Ramakrishnan in the Mathematical Sciences. The Legacy of Alladi Ramakrishnan in the Mathematical Sciences 275 292 .
F. Stevens, H. Vrielinck, V. Van Speybroeck, E. Pauwels, F. Callens & M. Waroquier. (2006) X - (X = O, S) Ions in Alkali Halide Lattices through Density Functional Calculations. 1. Substitutional Defect Models . The Journal of Physical Chemistry B 110:16, pages 8204-8212.
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S. Tyagi. (2005) New Series Representation for the Madelung Constant. Progress of Theoretical Physics 114:3, pages 517-521.
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F. Stevens, V. Van Speybroeck, E. Pauwels, H. Vrielinck, F. Callens & M. Waroquier. (2005) Level of theory study of magnetic resonance parameters of chalcogen XY − (X, Y = O, S and Se) defects in alkali halides . Phys. Chem. Chem. Phys. 7:2, pages 240-249.
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V. Van Speybroeck, E. Pauwels, F. Stevens, F. Callens & M. Waroquier. (2005) Study of radical defects in crystalline lattices from first-principles molecular dynamics simulations. International Journal of Quantum Chemistry 101:6, pages 761-769.
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Elsa Moggia & Bruno Bianco. (2004) Closed-form expression for the potential within a face centred cubic ionic crystal. Journal of Electrostatics 61:3-4, pages 269-280.
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Jonathan Michael Borwein & Kwok-Kwong Stephen Choi. 2003. Number Theory and Modular Forms. Number Theory and Modular Forms 95 127 .
F. Stevens, H. Vrielinck, F. Callens, E. Pauwels & M. Waroquier. (2002) Density-functional study of defects in alkali halides . Physical Review B 66:13.
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. (2009) Letters to the editor. The Mathematical Intelligencer 23:3, pages 3-6.
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