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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/17057

Title: Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green's function
Authors: Linton, C.M.
Issue Date: 2015
Publisher: © AIP Publishing LLC
Citation: LINTON, C.M., 2015. Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green's function. Journal of Mathematical Physics, 56 (1), 013505.
Abstract: A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green's function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of Θ-functions which are significant generalisations of known results.
Description: The following article appeared in Journal of Mathematical Physics, 2015, 56 (1), 013505 and may be found at http://dx.doi.org/10.1063/1.4905732. Copyright 2015 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Version: Published
DOI: 10.1063/1.4905732
URI: https://dspace.lboro.ac.uk/2134/17057
Publisher Link: http://dx.doi.org/10.1063/1.4905732
ISSN: 0022-2488
Appears in Collections:Published Articles (Maths)

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