Borwein, David and Borwein, Jonathan M. and Pinner, Christopher (1998) *Convergence of Madelung-Like Lattice Sums.* Trans. Amer. Math. Soc., 350 . pp. 3131-3167.

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## Abstract

We make a general study of the convergence properties of lattice sums, involving potentials, of the form occuring in Mathematical Chemistry and Physics. Many specific examples are studied in detail. The prototype is Madelung's constant for NaCl: $$\sum_{-\infty}^{\infty} \frac{(-1)^{n+m+p}} {\sqrt{n^2+m^2+p^2}} = -1.74756459 \cdots $$ presuming that one appropriately interprets the summation proccess.

Item Type: | Article |
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Additional Information: | pubdom FALSE |

Uncontrolled Keywords: | lattice sums, zeta functions, conditional convergence, Madelung's constant, Dirichlet series, theta functions |

Subjects: | 11-xx Number theory > 11Sxx Algebraic number theory: local and $p$-adic fields 30-xx Functions of a complex variable > 30Bxx Series expansion 40-xx Sequences, series, summability > 40Axx Convergence and divergence of infinite limiting processes 40-xx Sequences, series, summability > 40Bxx Multiple sequences and series 11-xx Number theory > 11Pxx Additive number theory, partitions |

Faculty: | UNSPECIFIED |

Depositing User: | Users 1 not found. |

Date Deposited: | 17 Nov 2003 |

Last Modified: | 13 Jan 2015 14:05 |

URI: | https://docserver.carma.newcastle.edu.au/id/eprint/104 |

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