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We consider a class of sums involving Bessel functions summed over the square array. The sums involve the length (ξ) of an arbitrary vector lying within the central unit cell. We establish conditions under which the sums reduce to polynomial forms in ξ (possibly with a single logarithmic term in addition), and show how these polynomials may be conveniently evaluated.
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Nicorovici et al. (1996) studied this question.
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