Further relations amongst infinite series and products. II. The evaluation of three-dimensional lattice sums

DOI10.1088/0305-4470/23/2/009zbMath0744.11048OpenAlexW2016154537MaRDI QIDQ4711970

I. J. Zucker

Publication date: 25 June 1992

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/23/2/009

zbMATH Keywords

Mellin transforminfinite series\(q\)-seriesinfinite productsPoisson transformthree-dimensional lattice sums

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Statistical mechanics of crystals (82D25) Theta series; Weil representation; theta correspondences (11F27) Analytic theory of partitions (11P82)

Related Items (11)

FOURIER SERIES OF A CLASS OF ETA QUOTIENTS ⋮ Systematic investigation of two-dimensional static array sums ⋮ Exact partition functions for deformed \( \mathcal{N}=2 \) theories with \( {\mathcal{N}}_f=4 \) flavours ⋮ Analogues of Jacobi's derivative formula ⋮ Iterated elliptic and hypergeometric integrals for Feynman diagrams ⋮ Holomorphic eta quotients of weight 1/2 ⋮ Dirichlet L -series with real and complex characters and their application to solving double sums ⋮ EXPLICIT FORMULAS FOR THE FOURIER COEFFICIENTS OF A CLASS OF ETA QUOTIENTS ⋮ Evaluation of some \(q\)-integrals in terms of the Dedekind eta function ⋮ Compressed lattice sums arising from the Poisson equation ⋮ New Representations for the Madelung Constant

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