OFFSET
0,2
REFERENCES
James Dodson, The Mathematical Repository Containing Analytical Solutions of Five Hundred Questions: Mostly Selected from Scarce and Valuable Authors, (1748), page 375.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
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 (5)
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.
Michael Penn, The solution is an important constant, YouTube video, 2021.
FORMULA
Equals Sum_{n>=1} 1/(2n)^3 = 1/8 + 1/64 + 1/216 + 1/512 + ...
Equals A002117/8.
zeta(3)/8 + A233091 = Sum_{n>=1} 1/(2n+1)^3 + Sum_{n>=1} 1/(2n)^3 = zeta(3).
Equals Sum_{k>=1} (-1)^(k+1) * H(k)/(k+1)^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, Jul 22 2020
Equals Integral_{x=0..Pi/4} log(sin(x))*log(cos(x))/(sin(x)*cos(x)) dx (Lord, 2005). - Amiram Eldar, Jun 23 2023
Equals -integral_{x=0..1} log(x) log(1+x)/(1+x). [Barbieri] - R. J. Mathar, Jun 07 2024
EXAMPLE
0.150257112894949285674967270188...
MATHEMATICA
RealDigits[(Zeta[3])/8, 10, 100][[1]]
PROG
(Sage) (zeta(3)/8).n(100)
(PARI) zeta(3)/8 \\ Michel Marcus, Sep 16 2016
(Magma) SetDefaultRealField(RealField(120)); L:=RiemannZeta(); Evaluate(L, 3)/8; // G. C. Greubel, Nov 24 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Terry D. Grant, Sep 15 2016
STATUS
approved