A251809 Decimal expansion of 3*sqrt(2)*Pi^3/128.

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).

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions for small moduli, Section 2.2 L(m=8, r=4, s=3).

Index entries for transcendental numbers.

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.

Cf. A093954, A188510.

Sequence in context: A329208 A153738 A159790 * A016639 A138341 A374525

Adjacent sequences: A251806 A251807 A251808 * A251810 A251811 A251812

Keyword

nonn,cons,changed

Author

Bruno Berselli, Dec 10 2014

Status

approved