Borwein J.M., Glasser M.L., McPhedran R.C., Wan J.G. Lattice Sums Then and Now

Cambridge University Press, UK, 2013. — 390 p. — (Encyclopedia of Mathematics and Its Applications 150) — ISBN: 1107039908.The study of lattice sums is an important topic in mathematics, physics, and other areas of science. It is not a new field, dating back at least to the work of Appell in 1884, and has attracted contributions from some of the most eminent practitioners of science. Despite this, it has not been widely recognized as an area with its own important tradition, results, and techniques. This has led to independent discoveries and rediscoveries of important formulae and methods and has.Lattice sums
Convergence of lattice sums and Madelung’s constant
Angular lattice sums
Use of Dirichlet series with complex characters
Lattice sums and Ramanujan’s modular equations
Closed-form evaluations of three- and four-dimensional sums
Electron sums
Madelung sums in higher dimensions
Seventy years of theWatson integrals
Appendixes
Tables of modular equations
Character table for Dirichlet L-series
Values of K[N] for all integer N from 1 to 100