A255986 Decimal expansion of Sum_{m,n >= 1} (-1)^(m + n)/(m*n*(m + n)).

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

Offset

0,1

Links

Table of n, a(n) for n=0..102.

David H. Bailey and Jonathan M. Borwein, Computation and structure of character polylogarithms with applications to character Mordell-Tornheim-Witten sums, Mathematics of Computation, Vol. 85, No. 297 (2016), pp. 295-324, alternative link.

Nick Lord, Problen 89.D, Problem Corner, The Mathematical Gazette, Vol. 89, No. 514 (2005), pp. 115-119; Solution, ibid., Vol. 89, No. 516 (2005), pp. 539-542.

Formula

Equals zeta(3)/4 = A002117/4.

From Amiram Eldar, Aug 07 2020: (Start)

Equals Integral_{x=0..oo} x^2/(exp(2*x) - 1) dx.

Equals Integral_{x=0..1} x * log(x)^2/(1 - x^2) dx. (End)

Equals Integral_{x=0..Pi/2} log(sin(x))*log(cos(x))/(sin(x)*cos(x)) dx (Lord, 2005). - Amiram Eldar, Jun 23 2023

Example

0.30051422578989857134993454037786249769124657308512472...

Maple

evalf(Zeta(3)/4, 120); # Vaclav Kotesovec, Mar 13 2015

Mathematica

digits = 103; s = NSum[(-1)^(m + n)/(m*n*(m + n)), {m, 1, Infinity}, {n, 1, Infinity}, WorkingPrecision -> digits+10, Method -> "AlternatingSigns"]; RealDigits[s, 10, digits] // First
RealDigits[Zeta[3]/4, 10, 100][[1]] (* Amiram Eldar, Aug 07 2020 *)

Crossrefs

Cf. A002117.

Sequence in context: A210953 A254280 A092669 * A011400 A362271 A115013

Adjacent sequences: A255983 A255984 A255985 * A255987 A255988 A255989

Keyword

nonn,cons

Author

Jean-François Alcover, Mar 13 2015

Status

approved