A185583 Decimal expansion of Sum_{m,n,p = -infinity..infinity} 4*(-1)^(m + n + p)/sqrt(m^2 + (2n-1/2)^2 + (2p-1/2)^2).

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

Offset

1,2

Links

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

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 j(1).

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 j(1).

Formula

Equals 8*Sum_{n>=1, p>=1} cosech(d*Pi)/d where d = sqrt((n-1/2)^2 + 2*(p-1/2)^2).

Example

1.285846549754779458631385161116...

Mathematica

digits = 105; Clear[f]; f[n_, p_] := f[n, p] = (d = Sqrt[(n - 1/2)^2 + 2*(p - 1/2)^2]; (Csch[d*Pi]/d) // N[#, digits + 10] &); f[m_] := f[m] = 8*Sum[f[n, p], {n, 1, m}, {p, 1, 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, A185581, A185582.

Sequence in context: A171044 A271886 A182528 * A309792 A318725 A155901

Adjacent sequences: A185580 A185581 A185582 * A185584 A185585 A185586

Keyword

nonn,cons

Author

R. J. Mathar, Jan 31 2011

Extensions

More terms from Jean-François Alcover, Feb 21 2013

Status

approved