Na. Nicorovici et al., ANALYTICAL RESULTS FOR A CLASS OF SUMS INVOLVING BESSEL-FUNCTIONS ANDSQUARE ARRAYS, Journal of mathematical physics, 37(4), 1996, pp. 2043-2052
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 whi
ch the sums reduce to polynomial forms in xi (possibly with a single l
ogarithmic term in addition), and show how these polynomials may be co
nveniently evaluated. (C) 1996 American Institute of Physics.