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

0,1

Links

Table of n, a(n) for n=0..99.

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

Example

0.99259381992283028267...

Mathematica

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

Prog

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

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.

Sequence in context: A199623 A255169 A019892 * A110639 A254273 A011211

Adjacent sequences: A275707 A275708 A275709 * A275711 A275712 A275713

Keyword

nonn,cons

Author

Terry D. Grant, Aug 06 2016

Status

approved