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A085469 Decimal expansion of Madelung constant (negated) for face-centered cubic lattice. 11
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; text; internal format)
OFFSET

1,2

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).

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

Leslie Glasser, Solid-State Energetics and Electrostatics: Madelung Constants and Madelung Energies, Inorg. Chem., 2012, 51 (4), 2420-2424; DOI: 10.1021/ic2023852

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.

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

Simon 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

Wikipedia, Madelung constant

Index entries for sequences related to f.c.c. lattice

FORMULA

Sum_{i, j, k not all 0} (-1)^(i+j+k)/sqrt(i^2+j^2+k^2).

EXAMPLE

-1.7475645946331821906362120355443974034851614366247417581528253507...

MATHEMATICA

RealDigits[ 12Pi*Sum[ Sech[Pi/2*Sqrt[(2j + 1)^2 + (2k + 1)^2]]^2, {j, 0, 40}, {k, 0, 40}], 10, 111][[1]] (* Robert G. Wilson v, Jul 12 2005 *)

CROSSREFS

Cf. A004015, A005875, A108778 (continued fraction).

Sequence in context: A194361 A153586 A153186 * A050996 A085541 A133055

Adjacent sequences:  A085466 A085467 A085468 * A085470 A085471 A085472

KEYWORD

nonn,cons,changed

AUTHOR

Eric W. Weisstein, Jul 01 2003

EXTENSIONS

Entry revised by N. J. A. Sloane, Apr 12, 2004

Definition corrected by Leslie Glasser, Jan 24 2011

STATUS

approved

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Last modified April 23 04:16 EDT 2014. Contains 240909 sequences.