Evaluation of lattice sums using Poisson's summation formula. III
- 1 November 1976
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 9 (11) , 1801-1810
- https://doi.org/10.1088/0305-4470/9/11/004
Abstract
For pt.II see ibid., vol.9, p.1411, 1976. Using Poisson's summation formula of dimensionality less than or equal to three, a number of slowly convergent three-dimensional lattice sums, which appear in the theory of ionic crystals, have been reduced to rapidly convergent two-dimensional sums. As a result, some of the formulae reported recently by Hautot (1974, 1975) and by Zucker (1975, 1976) are reproduced and several new ones which exhibit a remarkably fast convergence are obtained.Keywords
This publication has 6 references indexed in Scilit:
- Evaluation of lattice sums using Poisson's summation formula. IIJournal of Physics A: General Physics, 1976
- Functional equations for poly-dimensional zeta functions and the evaluation of Madelung constantsJournal of Physics A: General Physics, 1976
- Madelung constants and lattice sums for invariant cubic lattice complexes and certain tetragonal structuresJournal of Physics A: General Physics, 1975
- Evaluation of a class of lattice sums in arbitrary dimensionsJournal of Mathematical Physics, 1975
- New applications of Poisson's summation formulaJournal of Physics A: General Physics, 1975
- A new method for the evaluation of slowly convergent seriesJournal of Mathematical Physics, 1974