A247046 Decimal expansion of delta_3, a constant associated with a certain 3-dimensional lattice sum.

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 79.

Links

Table of n, a(n) for n=1..100.

Eric Weisstein's World of Mathematics, Lattice Sum.

Formula

Pi_0 + Pi/6, where Pi_0 is A185576.

Example

-2.313698703882320603588809874061155008356357135595965962...

Mathematica

digits = 100; k0 = 10; dk = 10; Clear[s]; s[k_] := s[k] = 7*(Pi/6) - 19/2*Log[2] + 4*Sum[(3 + 3*(-1)^m + (-1)^(m + n))*Csch[Pi*Sqrt[m^2 + n^2]]/Sqrt[m^2 + n^2], {m, 1, k}, {n, 1, k}] // N[#, digits + 10] &; s[k0]; s[k = k0 + dk]; While[RealDigits[s[k], 10, digits + 5][[1]] != RealDigits[s[k - dk], 10, digits + 5][[1]], Print["s(", k, ") = ", s[k]]; k = k + dk]; Pi0 = s[k]; delta3 = Pi0 + Pi/6; RealDigits[delta3, 10, digits] // First

Crossrefs

Cf. A088537, A185576, A247042.

Sequence in context: A176850 A208516 A111808 * A081422 A213742 A213743

Adjacent sequences: A247043 A247044 A247045 * A247047 A247048 A247049

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 10 2014

Status

approved