OFFSET
1,3
COMMENTS
Equals the value of the Dirichlet L-series of the non-principal character modulo 8 (A188510) at s=3. - Jianing Song, Nov 16 2019
REFERENCES
L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 64 (formula 340).
LINKS
FORMULA
Equals Sum_{i >= 0} (-1)^floor(i/2)/(2i+1)^3 = +1 +1/3^3 -1/5^3 -1/7^3 +1/9^3 +1/11^3 - ...
Equals Sum_{i >= 1} A188510(i)/i^3 = Sum_{i >= 1} Kronecker(-8,i)/i^3. - Jianing Song, Nov 16 2019
Equals 1/(Product_{p prime == 1 or 3 (mod 8)} (1 - 1/p^3) * Product_{p prime == 5 or 7 (mod 8)} (1 + 1/p^3)). - Amiram Eldar, Dec 17 2023
EXAMPLE
1.027722585936858567879256618002255767210100318536997465331084755185...
MATHEMATICA
RealDigits[3 Sqrt[2] Pi^3/128, 10, 90][[1]]
PROG
(PARI) 3*sqrt(2)*Pi^3/128 \\ G. C. Greubel, Jul 27 2018
(Magma) R:= RealField(); 3*Sqrt(2)*Pi(R)^3/128; // G. C. Greubel, Jul 27 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bruno Berselli, Dec 10 2014
STATUS
approved