Abstract
It is well known that, under certain circumstances, discrete plane waves can propagate through lattices. Waves can also be generated by oscillating one point in the lattice: the corresponding solution of the governing partial difference equations is the discrete Green’s function, g mn . The far-field behaviour of g mn is obtained using three methods: textbook derivations are corrected and a formula for g nn as a Legendre function is derived. The low-frequency behaviour of g mn is also obtained using Mellin transforms. These results are useful in the development of a discrete scattering theory.
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