A185581 Decimal expansion of 8*Sum_{m,n,p = -infinity..infinity} (-1)^(m + n + p)/ sqrt( (2*m-1/2)^2+(2*n-1/2)^2+(2*p-1/2)^2 ).

2, 5, 3, 3, 5, 5, 7, 4, 0, 4, 4, 3, 3, 1, 2, 1, 0, 2, 5, 2, 9, 4, 8, 6, 2, 7, 9, 5, 7, 1, 8, 9, 2, 9, 1, 1, 1, 1, 2, 9, 7, 9, 6, 9, 6, 3, 9, 8, 2, 7, 4, 9, 9, 5, 8, 9, 7, 0, 3, 6, 9, 7, 0, 6, 5, 3, 4, 5, 3, 6, 3, 0, 6, 1, 2, 0, 3, 5, 5, 6, 9, 7, 0, 8, 0, 1, 6, 4, 9, 3, 0, 6, 1, 0, 8, 8, 8, 1, 1, 3, 7, 1, 0, 4, 2

Offset

1,1

Comments

The formula for g(1) in the 1976 paper on page 503 is a factor 2 too large.

Links

Table of n, a(n) for n=1..105.

I. J. Zucker, Madelung constants and lattice sums for invariant cubic lattice complexes and certain tetragonal structures, J. Phys. A: Math. Gen. 8 (11) (1975) 1734, variable g(1).

I. J. Zucker, Functional equations for poly-dimensional zeta functions and the evaluation of Madelung constants, J. Phys. A: Math. Gen. 9 (4) (1976) 499, variable g(1).

Formula

Equals 2*sqrt(2)*Sum_{n,p = -infinity..infinity} (-1)^n*cosech(d*Pi)/d where d = sqrt( (2*n-1/2)^2/2 + (p-1/2)^2 ).

Example

2.533557404433121025294862795718...

Mathematica

digits = 105; Clear[f]; f[n_, p_] := f[n, p] = (d = Sqrt[(2 n - 1/2)^2/2 + (p - 1/2)^2]; (-1)^n*(Csch[d*Pi]/d) // N[#, digits + 10] &); f[m_] := f[m] = 2 Sqrt[2]*Sum[f[n, p], {n, -m, m}, {p, -m, m}] // RealDigits[#, 10, digits + 10] & // First; f[0]; f[m = 10]; While[ f[m] != f[m - 10], Print[m]; m = m + 10]; f[m][[1 ;; digits]] (* Jean-François Alcover, Feb 21 2013 *)

Crossrefs

Cf. A185576, A185577, A185578, A185579, A185580, A185582, A185583.

Sequence in context: A069998 A162405 A141637 * A151960 A281300 A115320

Adjacent sequences: A185578 A185579 A185580 * A185582 A185583 A185584

Keyword

cons,nonn

Author

R. J. Mathar, Jan 31 2011

Extensions

More terms from Jean-François Alcover, Feb 21 2013

Status

approved