We consider sums arising in doubly quasiperiodic Green's functions for the Laplace equation, over the square array. The sums are represented as Fourier series, and it is shown that the coefficients in the series can be obtained as polynomials. We give expressions from which the first six array sums can be evaluated efficiently, and accurate to better than one part in 10(7), over most of the Brillouin zone. (C) 2002 American Institute of Physics. [References: 11]
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