Burrows ACooper SSchwerdtfeger P2023-11-122023-11-202022-11-162023-11-122023-11-202022-11-30Burrows A, Cooper S, Schwerdtfeger P. (2022). The Madelung constant in N dimensions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 478. 2267.1364-5021https://mro.massey.ac.nz/handle/10179/69174We 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.(c) The author/s CC BY 4.0https://creativecommons.org/licenses/by/4.0/Madelung constantlattice sums,NdimensionsJournal article10.1098/rspa.2022.03341471-2946journal-article20220334