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A185580 Decimal expansion of Sum_{m,n,p = -infinity..infinity} (-1)^(m+n)/sqrt( m^2 + n^2 + (p-1/2)^2 ). 7

%I

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

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

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

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

%H I. J. Zucker, <a href="https://dx.doi.org/10.1088/0305-4470/8/11/008">Madelung constants and lattice sums for invariant cubic lattice complexes and certain tetragonal structures</a>, J. Phys. A: Math. Gen. 8 (11) (1975) 1734, variable f(1).

%H I. J. Zucker, <a href="http://dx.doi.org/10.1088/0305-4470/9/4/006">Functional equations for poly-dimensional zeta functions and the evaluation of Madelung constants</a>, J. Phys. A: Math. Gen. 9 (4) (1976) 499, variable f(1).

%F Equals 4*Sum_{n>=1, p>=1} cosech(d*Pi)/d where d = sqrt((n-1/2)^2 + (p-1/2)^2).

%t digits = 105; Clear[f]; f[n_, p_] := f[n, p] = (d = Sqrt[(n - 1/2)^2 + (p - 1/2)^2]; (Csch[d*Pi]/d) // N[#, digits + 10] &); f[m_] := f[m] = 4*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-Fran├žois Alcover_, Feb 21 2013 *)

%Y Cf. A185576, A185577, A185578, A185579, A185581, A185582, A185583.

%K cons,nonn

%O 1,2

%A _R. J. Mathar_, Jan 31 2011

%E More terms from _Jean-Fran├žois Alcover_, Feb 21 2013

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Last modified May 20 05:35 EDT 2019. Contains 323418 sequences. (Running on oeis4.)