

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
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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 facecentered 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 7379.
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), 481509.
R. E. Crandall and J. P. Buhler, Elementary function expansions for Madelung constants, J. Phys. A: Math. Gen. 20 (1987) no. 16, 54975510.
R. E. Crandall and J. P. Buhler, The potential within a crystal lattice, J. Phys. A: Math. Gen. 20 (1987) no. 9, 22792292.
E. R. Fuller Jr and E. R. Naimon, Electrostatic Contributions to the BruggerType Elastic Constants, Phys. Rev. B 6 (1971) no. 10, 36093620.
Leslie Glasser, SolidState Energetics and Electrostatics: Madelung Constants and Madelung Energies, Inorg. Chem., 2012, 51 (4), 24202424; DOI: 10.1021/ic2023852.
André Hautot, New applications of Poisson's summation formula, J of Phys, A vol. 8 #6, 1975 pp. 853862.
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, 517521.
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



