OFFSET
0,1
COMMENTS
This constant is irrational by Apéry's theorem. - Charles R Greathouse IV, Feb 11 2024
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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 (4)
Su Hu, Min-soo Kim, Euler's integral, multiple cosine function and zeta values, arXiv:2201.011247 (2023), series last equation.
Seán Stewart, Problem 12206, The American Mathematical Monthly, Vol. 127, No. 8 (2020), p. 752.
Wikipedia, Dirichlet eta function.
FORMULA
Equals 3*zeta(3)/4 = 3*A002117/4.
Also equals the integral over the unit cube [0,1]x[0,1]x[0,1] of 1/(1+x*y*z) dx dy dz. - Jean-François Alcover, Nov 24 2014
Equals Sum_{n>=1} (-1)^(n+1)/n^3. - Terry D. Grant, Aug 03 2016
Equals Sum_{n>=1} AH(2*n)/n^2, where AH(n) = Sum_{k=1..n} (-1)^(k+1)/k = A058313(n)/A058312(n) is the n-th alternating harmonic number (Stewart, 2020). - Amiram Eldar, Oct 04 2021
Equals -int_0^1 log(x)log(1+x)/x dx [Barbieri] - R. J. Mathar, Jun 07 2024
EXAMPLE
0.9015426773696957140498036211335874930737...
MAPLE
3*Zeta(3)/4 ; evalf(%) ;
MATHEMATICA
RealDigits[3(Zeta[3])/4, 10, 75][[1]] (* Bruno Berselli, Dec 20 2011 *)
PROG
(PARI) -polylog(3, -1) \\ Charles R Greathouse IV, Mar 28 2012
(PARI) 3/4*zeta(3) \\ Charles R Greathouse IV, Mar 28 2012
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Oct 09 2011
STATUS
approved