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Journal of Physics A: Mathematical and General Volume 38 Number 31 Create an alert RSS this journal

Sandeep Tyagi 2005 J. Phys. A: Math. Gen. 38 6987 doi:10.1088/0305-4470/38/31/008

Rapid evaluation of the periodic Green function in d dimensions

Sandeep Tyagi

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Abstract References Cited By

A method is given to obtain the Green function for the Poisson equation in any arbitrary integer dimension under periodic boundary conditions. We obtain recursion relations which relate the solution in d-dimensional space to that in (d − 1)-dimensional space. Near the origin, the Green function is shown to split into two parts, one is the essential Coulomb singularity and the other is regular. We are thus able to give representations of the Coulomb sum in higher dimensions without recourse to any integral representations. The expressions converge exponentially fast in all parts of the simulation cell. Works of several authors are shown to be special cases of this more general method.


PACS

02.30.Lt Sequences, series, and summability

02.30.Gp Special functions

MSC

33C10 Bessel and Airy functions, cylinder functions, 0F1

Subjects

Mathematical physics

Dates

Issue 31 (5 August 2005)

Received 2 June 2005, in final form 21 June 2005

Published 20 July 2005



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