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 A185579 Decimal expansion of Sum_{m,n,p = -infinity..infinity} (-1)^m/sqrt(m^2 + (n-1/2)^2 + (p-1/2)^2). 7

%I

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

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

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

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

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

%e 1.5401709018555436174364666638648...

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

%Y Cf. A185576, A185577, A185578, A185580, A185581, A185582, A185583.

%K cons,nonn

%O 1,2

%A _R. J. Mathar_, Jan 31 2011

%E More terms from _Jean-François Alcover_, Feb 21 2013

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Last modified June 20 10:13 EDT 2019. Contains 324234 sequences. (Running on oeis4.)