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 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). 7
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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 * A318725 A155901 A029745 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

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Last modified May 19 05:05 EDT 2019. Contains 323377 sequences. (Running on oeis4.)