OFFSET
0,1
LINKS
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.
R. Barbieri, J. A. Mignaco and E. Remiddi, Electron form factors up to fourth order. I., Il Nuovo Cim. 11A (4) (1972) 824-864, table II (10).
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.
R. J. Mathar, Some definite integrals over a power multiplied by four modified Bessel functions, vixra:1606.0141 (2016) eq (28).
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
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Mar 13 2015
STATUS
approved