A346927 Decimal expansion of the Dirichlet eta function at 10.

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

Offset: 0

Author

Sean A. Irvine, Aug 07 2021

Keywords

• nonn
• cons

Examples

			0.999039507598271565639221845699341831425929649666890...
		

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, A347150, A347059.

Programs

Mathematica

RealDigits[DirichletEta[10], 10, 100][[1]] (* Amiram Eldar, Aug 08 2021 *)

PARI

-polylog(10, -1) \\ Michel Marcus, Aug 08 2021

Formula

Equals 73 * Pi^10 / (2^9 * 3^5 * 5 * 11).

Equals (511/512) * zeta(10).

Equals Sum_{k>=1} (-1)^(k+1) / k^10.

Equals eta(10).