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A085469
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Decimal expansion of Madelung constant (negated) for face-centered cubic lattice.
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8
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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, 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, 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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is the electrostatic potential at the origin produced by unit charges of sign (-1)^(i+j+k) at all nonzero lattice points (i,j,k).
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REFERENCES
| Richard E. Crandall, Topics in Advanced Scientific Computation, Springer, Telos books, 1996. pages 73-79.
S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 76
Andre Hautot, New applications of Poisson's summation formula, J of Phys, A vol. 8 #6, 1975 pp. 853-862.
Sadri Hassani, Mathematical Methods Using Mathematica: For Students of Physics and Related Fields, Springer, NY, page 60.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1847
D. H. Bailey, J. M. Borwein, V. Kapoor and E. Weisstein, Ten Problems in Experimental Mathematics, Amer. Math. Monthly 113 (6) (2006), 481-509.
R. E. Crandall and J. P. Buhler, Elementary function expansions for Madelung constants,J. Phys. A: Math. Gen. 20 (1987) no 16, 5497-5510
R. E. Crandall and J. P. Buhler, The potential within a crystal lattice, J. Phys. A: Math. Gen. 20 (1987) no 9, 2279-2292
E. R. Fuller Jr and E. R. Naimon, Electrostatic Contributions to the Brugger-Type Elastic Constants,Phys. Rev. B 6 (1971) no 10, 3609-3620
Simon Plouffe, Madelung constant
S. Plouffe, The Levy constant
Sandeep Tyagi, New series representation of the Madelung constant, Prog. Theor. Phys. 114 (2005) No 3, 517-521
Eric Weisstein's World of Mathematics, Benson's Formula
Eric Weisstein's World of Mathematics, Madelung Constants
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FORMULA
| Sum_{i, j, k not all 0} (-1)^(i+j+k)/sqrt(i^2+j^2+k^2).
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EXAMPLE
| -1.7475645946331821906362120355443974034851614366247417581528253507...
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MATHEMATICA
| 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)
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CROSSREFS
| Cf. A004015, A005875.
Cf. A108778 = continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 13 2009]
Sequence in context: A194361 A153586 A153186 * A050996 A085541 A133055
Adjacent sequences: A085466 A085467 A085468 * A085470 A085471 A085472
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KEYWORD
| nonn,cons
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Jul 01, 2003
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EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 12, 2004
Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
PARI code removed by D. S. McNeil (mcneil(AT)hku.hk), Dec 26 2010
Definition corrected by Leslie Glasser, Jan 24 2011
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