A334668 -id:A334668 - cp's OEIS frontend

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

Terry D. Grant, Aug 06 2016

			0.99259381992283028267...

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.

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

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

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

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

A334669 Denominator of Sum_{k=1..n} (-1)^(k+1)/k^7.

Original entry on oeis.org

1, 128, 279936, 35831808, 2799360000000, 2799360000000, 2305393332480000000, 295090346557440000000, 645362587921121280000000, 645362587921121280000000, 12576291107821424895098880000000, 12576291107821424895098880000000, 789143616376081512994335288360960000000

Offset: 1

Petros Hadjicostas, May 07 2020

Lim_{n -> infinity} A334668(n)/a(n) = A275710 = (63/64)*A013665.

			The first few fractions are 1, 127/128, 277877/279936, 35566069/35831808, 2778634972433/2799360000000, 2778624972433/2799360000000, ... = A334668/A334669.

Michael De Vlieger, Table of n, a(n) for n = 1..336

Cf. A013665, A275710, A334668 (numerators).

Denominator @ Accumulate[Table[(-1)^(k + 1)/k^7, {k, 1, 13}]] (* Amiram Eldar, May 08 2020 *)

a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^7)); \\ Michel Marcus, May 08 2020

cp's OEIS Frontend

A275710 Decimal expansion of the Dirichlet eta function at 7.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Sage

Formula