A275710 Decimal expansion of the Dirichlet eta function at 7.

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

Offset: 0

Author

Terry D. Grant, Aug 06 2016

Keywords

• nonn
• cons

Examples

			0.99259381992283028267...
		

Crossrefs

Cf. A002162 (value at 1), A013665, A072691 (value at 2), A197070 (value at 3), A267315 (value at 4), A267316 (value at 5), A275703 (value at 6), A334668, A334669, A347150, A347059.

Programs

Mathematica

RealDigits[63 Zeta[7]/64, 10, 100] [[1]]

PARI

-polylog(7, -1) \\ Michel Marcus, Aug 20 2021

Sage

s = RLF(0); s
RealField(110)(s)
for i in range(1, 10000): s -= (-1)^i / i^7
print(s) # Terry D. Grant, Aug 06 2016

Formula

eta(7) = 63*zeta(7)/64 = (63*A013665)/64.

eta(7) = Lim_{n -> infinity} A334668(n)/A334669(n). - Petros Hadjicostas, May 07 2020

Equals Sum_{k>=1} (-1)^(k+1) / k^7. - Sean A. Irvine, Aug 19 2021