Compressed lattice sums arising from the Poisson equation

DOI10.1186/1687-2770-2013-75zbMath1294.11137OpenAlexW2109885393WikidataQ59304977 ScholiaQ59304977MaRDI QIDQ2017354

David H. Bailey, Jonathan M. Borwein

Publication date: 25 June 2014

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-2770-2013-75

zbMATH Keywords

Poisson equationlattice sumsexperimental mathematicshigh-precision computation

Mathematics Subject Classification ID

Asymptotic expansions of solutions to PDEs (35C20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Trigonometric and exponential sums (general theory) (11L03)

Related Items (4)

Jonathan Borwein: Experimental Mathematician ⋮ Jonathan Borwein: Renaissance Mathematician ⋮ Computer Discovery and Analysis of Large Poisson Polynomials ⋮ Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

Cites Work

• Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi
• Parallel integer relation detection: Techniques and applications
• Some Infinite Series of Exponential and Hyperbolic Functions
• Dirichlet L -series with real and complex characters and their application to solving double sums
• A systematic way of converting infinite series into infinite products
• Functional equations for poly-dimensional zeta functions and the evaluation of Madelung constants
• Further relations amongst infinite series and products. II. The evaluation of three-dimensional lattice sums

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