A347150 Decimal expansion of the Dirichlet eta function at 8.

9, 9, 6, 2, 3, 3, 0, 0, 1, 8, 5, 2, 6, 4, 7, 8, 9, 9, 2, 2, 7, 2, 8, 9, 2, 6, 0, 0, 8, 2, 8, 0, 3, 6, 1, 7, 8, 7, 4, 1, 2, 5, 1, 5, 9, 4, 7, 2, 8, 9, 8, 0, 6, 7, 0, 4, 5, 2, 8, 9, 0, 2, 9, 1, 9, 4, 3, 5, 9, 6, 4, 8, 2, 5, 7, 7, 5, 8, 5, 8, 9, 2, 8, 2, 8, 2, 4

Offset: 0

Author

Sean A. Irvine, Aug 19 2021

Keywords

• nonn
• cons

Examples

			0.9962330018526478992272892600828036178741251594728980...
		

References

• L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (306).

Links

• Michael I. Shamos, Shamos's catalog of the real numbers (2011).
• Index entries for transcendental numbers

Crossrefs

Cf. A072691, A197070, A267315, A267316, A275703, A275710, A346927, A347059.

Programs

Mathematica

RealDigits[DirichletEta[8], 10, 100][[1]] (* Amiram Eldar, Aug 20 2021 *)

PARI

-polylog(8, -1) \\ Michel Marcus, Aug 20 2021

Formula

Equals (127/128) * zeta(8).

Equals 127 * Pi^8 / 1209600.

Equals Sum_{k>=1} (-1)^(k+1) / k^8.

Equals eta(8).