OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Sections 1.6.3 and 1.6.8, pp. 43 and 47.
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
Equals Integral_{x=1..2} log(x)^2/(x-1) dx [Ramanujan] (see Finch). - Stefano Spezia, Nov 03 2024
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 *)
PROG
(PARI) zeta(3)/4 \\ Stefano Spezia, Nov 02 2024
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Mar 13 2015
STATUS
approved