STATUS
reviewed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
reviewed
approved
proposed
reviewed
editing
proposed
eta(6) = 31*(Pi^6)/30240 = 31*A092732/30240 = Sum _{n>=1} (-1)^(n+1)/n^6.
eta(6) = Lim_lim_{n -> infinity} A136677(n)/A334605(n). - Petros Hadjicostas, May 07 2020
reviewed
editing
proposed
reviewed
editing
proposed
RealDigits[31*(piPi^6)/30240, 10, 100]
approved
editing
proposed
approved
editing
proposed
It appears that each sum of a Dirichlet eta function is 1/2^(x-1) less than the Zeta value, zeta(x), where x is a positive integer > 1. In this case, neta(x) = neta(6) = (31/32)*zeta(6) = 31*(Pi^6)/30240. Therefore neta(6) = 1/2^(6-1) or 1/32nd less than zeta(6) (see A013664). [Edited by _Petros Hadjicostas_, May 07 2020]
neta(6) = 31*(Pi^6)/30240 = 31*A092732/30240 = Sum {n>=1} (-1)^(n+1)/n^6.
Equals eta(6) = Lim_{n -> infinity} A136677(n)/A334605(n). - Petros Hadjicostas, May 07 2020