000			03348nam a2200469 i 4500
001			EBC1394585
003			MiAaPQ
005			20240120144548.0
006			m o d |
007			cr cnu||||||||
008			130326s2013 enkad ob 001 0 eng|d
020			_z9781107039902 (hardback)
020			_a9781107421141 _q(electronic bk.)
035			_a(MiAaPQ)EBC1394585
035			_a(Au-PeEL)EBL1394585
035			_a(CaPaEBR)ebr10774095
035			_a(CaONFJC)MIL538459
035			_a(OCoLC)858903141
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA171.5 _b.B67 2013
082	0		_a511.3/3 _223
100	1		_aBorwein, Jonathan M.
245	1	0	_aLattice sums then and now / _cJ.M. Borwein, University of Newcastle, New South Wales [and four others].
264		1	_aCambridge : _bCambridge University Press, _c2013.
300			_a1 online resource (390 pages) : _billustrations (some color).
336			_atext _2rdacontent
337			_acomputer _2rdamedia
338			_aonline resource _2rdacarrier
490	1		_aEncyclopedia of mathematics and its applications ; _v150
504			_aIncludes bibliographical references and index.
505	8		_aMachine generated contents note: 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 four-dimensional sums; 7. Electron sums; 8. Madelung sums in higher dimensions; 9. 70 years of the Watson integrals; Appendix A. Tables; Bibliography; Index.
520			_a"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"-- _cProvided by publisher.
588			_aDescription based on print version record.
590			_aElectronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.
650		0	_aLattice theory.
650		0	_aNumber theory.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aBorwein, Jonathan M. _tLattice sums then and now. _dCambridge : Cambridge University Press, 2013 _hxix, 368 pages _kEncyclopedia of mathematics and its applications ; 150 _z9781107039902 _w(DLC) 2013002993
797	2		_aProQuest (Firm)
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 150.
856	4	0	_uhttps://ebookcentral.proquest.com/lib/bacm-ebooks/detail.action?docID=1394585 _zClick to View
999			_c101647 _d101647