Journal of Computational Physics
Computational strategies for the Riemann zeta function
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Efficient computation of the 2D periodic Green's function using the Ewald method
Journal of Computational Physics
Journal of Computational Physics
One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation
Journal of Computational Physics
Photonic Crystals: Molding the Flow of Light
Photonic Crystals: Molding the Flow of Light
An integral representation of the Green function for a linear array of acoustic point sources
Journal of Computational Physics
Algorithm 926: Incomplete Gamma Functions with Negative Arguments
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Journal of Computational Physics
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A survey of different representations for lattice sums for the Helmholtz equation is made. These sums arise naturally when dealing with wave scattering by periodic structures. One of the main objectives is to show how the various forms depend on the dimension $d$ of the underlying space and the lattice dimension $d_\Lambda$. Lattice sums are related to, and can be calculated from, the quasi-periodic Green's function and this object serves as the starting point of the analysis.