Lattice sums then and now
 Author/Creator
 Borwein, Jonathan M.
 Language
 English.
 Publication
 Cambridge : Cambridge University Press, 2013.
 Physical description
 xix, 368 pages : illustrations ; 24 cm.
 Series
 Encyclopedia of mathematics and its applications ; 150.
Access
Available online

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QA171.5 .B67 2013

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QA171.5 .B67 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (pages [350]363) and index.
 Contents

 Foreword Preface 1. Lattice sums 2. Convergence of lattice sums and Madelung's constant 3. Angular lattice sums 4. Use of Dirichlet series with Complex characters 5. Lattice sums and Ramanujan's modular equations 6. Closed form evaluations of three and fourdimensional sums 7. Electron sums 8. Madelung sums in higher dimensions 9. 70 years of the Watson integrals Appendix A. Tables Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of knowledge that exists on lattice sums and their applications. The authors also provide commentaries on open questions, and explain modern techniques which simplify the task of finding new results in this fascinating and ongoing field. Lattice sums in one, two, three, four and higher dimensions are covered.
(source: Nielsen Book Data)  Supplemental links
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Bibliographic information
 Publication date
 2013
 Responsibility
 J.M. Borwein, University of Newcastle, New South Wales, M.L. Glasser, Clarkson University, New York, R.C. McPhedran, University of Sydney, J.G. Wan, Singapore University of Technology and Design, I.J. Zucker, King's College London.
 Series
 Encyclopedia of mathematics and its applications ; 150
 ISBN
 9781107039902
 1107039908
 9781306072083
 9781107418578
 1306072085
 1107418577