The Madelung constant in N dimensions
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Date
2022-11-30
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Royal Society
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CC BY 4.0
Abstract
We introduce two convergent series expansions (direct and recursive) in terms of Bessel functions and the number of representations of an integer as a sum of squares for N-dimensional Madelung constants, MN(s), where s is the exponent of the Madelung series (usually chosen as s=1/2). The convergence of the Bessel function expansion is discussed in detail. Values for MN(s) for s=1/2,3/2,3 and 6 for dimension up to N=20 are presented. This work extends Zucker's original analysis on N-dimensional Madelung constants for even dimensions up to N=8.
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Keywords
Madelung constant, lattice sums,, Ndimensions
Citation
Burrows A, Cooper S, Schwerdtfeger P. (2022). The Madelung constant in N dimensions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 478. 2267.