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A251809
Decimal expansion of 3*sqrt(2)*Pi^3/128.
10
1, 0, 2, 7, 7, 2, 2, 5, 8, 5, 9, 3, 6, 8, 5, 8, 5, 6, 7, 8, 7, 9, 2, 5, 6, 6, 1, 8, 0, 0, 2, 2, 5, 5, 7, 6, 7, 2, 1, 0, 1, 0, 0, 3, 1, 8, 5, 3, 6, 9, 9, 7, 4, 6, 5, 3, 3, 1, 0, 8, 4, 7, 5, 5, 1, 8, 5, 2, 5, 7, 7, 7, 2, 4, 6, 8, 5, 8, 4, 9, 6, 8, 0, 3, 5, 1
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).
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
Cf. A153071: Sum_{i >= 0} (-1)^i/(2i+1)^3.
Cf. A233091: Sum_{i >= 0} 1/(2i+1)^3.
Sequence in context: A329208 A153738 A159790 * A016639 A138341 A374525
KEYWORD
nonn,cons
AUTHOR
Bruno Berselli, Dec 10 2014
STATUS
approved