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, M N ( 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 M N ( 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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