Analytical results for a class of sums involving Bessel functions and square arrays

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