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A085469 Decimal expansion of Madelung constant (negated) for NaCl structure. 18
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).

The NaCl structure consists of two interpenetrating face-centered cubic lattices of ions with charges +1 and -1, together occupying all the sites of the simple cubic lattice. - Andrey Zabolotskiy, Oct 21 2019

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.

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.

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

André Hautot, New applications of Poisson's summation formula, J of Phys, A vol. 8 #6, 1975 pp. 853-862.

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: A153586 A319883 A153186 * A050996 A085541 A133055

Adjacent sequences:  A085466 A085467 A085468 * A085470 A085471 A085472

KEYWORD

nonn,cons

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

Definition corrected by Andrey Zabolotskiy, Oct 21 2019

STATUS

approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)