%I A085469
%S A085469 1,7,4,7,5,6,4,5,9,4,6,3,3,1,8,2,1,9,0,6,3,6,2,1,2,0,3,5,5,4,4,3,9,7,4,
%T A085469 0,3,4,8,5,1,6,1,4,3,6,6,2,4,7,4,1,7,5,8,1,5,2,8,2,5,3,5,0,7,6,5,0,4,0,
%U A085469 6,2,3,5,3,2,7,6,1,1,7,9,8,9,0,7,5,8,3,6,2,6,9,4,6,0,7,8,8,9,9,3
%N A085469 Decimal expansion of Madelung constant (negated) for simple cubic lattice.
%C A085469 This is the electrostatic potential at the origin produced by unit charges 
               at all nonzero lattice points.
%D A085469 Richard E. Crandall, Topics in Advanced Scientific Computation, Springer, 
               Telos books, 1996. pages 73-79.
%D A085469 S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 76
%D A085469 Andre Hautot, New applications of Poisson's summation formula, J of Phys, 
               A vol. 8 #6, 1975 pp. 853-862.
%D A085469 Sadri Hassani, Mathematical Methods Using Mahematica: For Students of 
               Physics and Related Fields, Springer, NY, page 60.
%H A085469 Harry J. Smith, <a href="b085469.txt">Table of n, a(n) for n=1,...,1847</
               a>
%H A085469 D. H. Bailey, J. M. Borwein, V. Kapoor and E. Weisstein, <a href="http:/
               /eprints.cecm.sfu.ca/archive/00000270/">Ten Problems in Experimental 
               Mathematics</a>
%H A085469 R. E. Crandall and J. P. Buhler, <a href="http://dx.doi.org/10.1088/0305-4470/
               20/16/024">Elementary function expansions for Madelung constants</
               a>,J. Phys. A: Math. Gen. 20 (1987) no 16, 5497-5510
%H A085469 R. E. Crandall and J. P. Buhler, <a href="http://dx.doi.org/10.1088/0305-4470/
               20/9/016">The potential within a crystal lattice</a>,J. Phys. A: 
               Math. Gen. 20 (1987) no 9, 2279-2292
%H A085469 E. R. Fuller Jr and E. R. Naimon, <a href="http://dx.doi.org/10.1103/
               PhysRevB.6.3609">Electrostatic Contributions to the Brugger-Type 
               Elastic Constants</a>,Phys. Rev. B 6 (1971) no 10, 3609-3620
%H A085469 Simon Plouffe, <a href="http://pi.lacim.uqam.ca/piDATA/madelung.txt">
               Madelung constant</a>
%H A085469 S. Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/
               math/MiscellaneousMathematicalConstants/chap55.html">The Levy constant</
               a>
%H A085469 Sandeep Tyagi, <a href="http://dx.doi.org/10.1143/PTP.114.517">New series 
               representation of the Madelung constant</a>, Prog. Theor. Phys. 114 
               (2005) No 3, 517-521
%H A085469 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BensonsFormula.html">Benson's Formula</a>
%H A085469 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MadelungConstants.html">Madelung Constants</a>
%F A085469 Sum_{i, j, k not all 0} (-1)^(i+j+k)/sqrt(i^2+j^2+k^2).
%e A085469 -1.7475645946331821906362120355443974034851614366247417581528253507...
%t A085469 RealDigits[ 12Pi*Sum[ Sech[Pi/2*Sqrt[(2j + 1)^2 + (2k + 1)^2]]^2, {j, 
               0, 40}, {k, 0, 40}], 10, 111][[1]] (from Robert G. Wilson v (rgwv(at)rgwv.com), 
               Jul 12 2005)
%o A085469 Contribution from Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 15 
               2009: (Start)
%o A085469 (PARI) { default(realprecision,1848); Madelung=-1.7475645946331821906362120355443974034851614366247417581\
%o A085469 5282535076504062353276117989075836269460788993083258153875371059328\
%o A085469 2029944183828013036933002156599363282376607172297568659238037167203\
%o A085469 8104106034214556064382777786832173132243697558773426250474787821285\
%o A085469 0860567916681675739924476841297036782518576281093713133720767071931\
%o A085469 9742497158115723096992309669273949657781107222671520547409011506891\
%o A085469 5716583082820050184892117803134673122964985828828184357133159143170\
%o A085469 0549563253348875363026704256274869484380028002592700268475574364975\
%o A085469 5049224613623992040015750630397214664811151237364010295066011939046\
%o A085469 7194373312530445102911514639759331918047977946099333746429426562908\
%o A085469 9693447792968854190440791425583272199718409067468023761538935445655\
%o A085469 0360273028544084934430280626704418241200439741867661772447563953444\
%o A085469 2306853849527943580751895490309305073843954464206438717926390780392\
%o A085469 0744282097957917736992304082214374645668043105692663197550459224432\
%o A085469 4807489408062474936107093630914922436898693314090379682324079004628\
%o A085469 4485812201497496519179081118204181820099174737652482957295684972796\
%o A085469 0238432587361742516304301213253823307779481444598420343673216212916\
%o A085469 2257903116101353527417534916776824438057139382407124829068734888254\
%o A085469 4125452570636795213611364128355999680725389089412120267587472631283\
%o A085469 4068262537606780890814341434286117388903537106985249308735988759660\
%o A085469 2363184706607516442145683455586623676605437844742512217481810852938\
%o A085469 2986359330038858941133489312302314299432802377837641811377123806642\
%o A085469 4808681158556451188180538368104068069306152452657895325624057864079\
%o A085469 5650016172016637963148270800941668173022273735813292616204948281860\
%o A085469 4313652035571121839219375759423906825690022886650812437760991098879\
%o A085469 3853419448765682333487553786009201932911164565934512096197118655146\
%o A085469 2827591256212354525900502281084479644187471007265894559896882147628\
%o A085469 71074726392395758480653025376082029590142679877534; x=-Madelung; for 
               (n=1, 1847, d=floor(x); x=(x-d)*10; write("b085469.txt", n, " ", 
               d)); } (End)
%Y A085469 Cf. A005875.
%Y A085469 Cf. A108778 = Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 13 2009]
%Y A085469 Sequence in context: A160575 A153586 A153186 this_sequence A050996 A085541 
               A133055
%Y A085469 Adjacent sequences: A085466 A085467 A085468 this_sequence A085470 A085471 
               A085472
%K A085469 nonn,cons
%O A085469 1,2
%A A085469 Eric Weisstein (eric(AT)weisstein.com), Jul 01, 2003
%E A085469 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 12, 
               2004
%E A085469 Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 19 2009