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A210593
Decimal expansion of the series limit of Sum_{k>=1} (-1)^k*log(k)/k^2.
6
1, 0, 1, 3, 1, 6, 5, 7, 8, 1, 6, 3, 5, 0, 4, 5, 0, 1, 8, 8, 6, 0, 0, 2, 8, 8, 2, 2, 1, 2, 2, 4, 2, 1, 8, 3, 6, 5, 9, 3, 8, 4, 7, 7, 6, 3, 7, 4, 9, 1, 1, 1, 6, 3, 3, 3, 4, 2, 9, 4, 2, 4, 7, 1, 9, 6, 2, 0, 4, 5, 3, 0, 9, 2, 0, 5, 4, 3, 6, 3, 2, 4, 9, 5, 3, 1, 7, 8, 0, 1, 2, 5, 3, 1, 9, 0, 3, 5, 6, 3, 9, 8, 2, 3, 1
OFFSET
0,4
COMMENTS
First derivative of the Dirichlet eta-function eta(s) at s=2.
Phatisena et al. misspell "Euler" and provide the wrong sign and an invalid 7th digit.
LINKS
S. Phatisena, R. E. Amritkar, P. V. Panat, Exchange and correlation potential for a two-dimensional electron gas at finite temperatures, Phys. Rev. A 34 (1986) 5070.
FORMULA
Decimal expansion of (log(2)*zeta(2) + zeta'(2)) / 2.
EXAMPLE
0.101316578163504501886002882212242183659384776374911163334294247196204...
MAPLE
1/2*log(2)*Zeta(2)+Zeta(1, 2)/2 ; evalf(%) ;
MATHEMATICA
N[(1/12)*Pi^2*(Log[4] - 12*Log[Glaisher] + Log[Pi] + EulerGamma), 105] // RealDigits // First (* Jean-François Alcover, Feb 05 2013 *)
PROG
(PARI) (log(2)*zeta(2)+zeta'(2))/2 \\ Charles R Greathouse IV, Mar 28 2012
CROSSREFS
Cf. A073002, A013661, A002162, A091812 (s=1), A375506 (s=3/2), A349220 (s=3), A349252 (s=4).
Sequence in context: A210602 A210801 A153091 * A179069 A235706 A124847
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Mar 23 2012
EXTENSIONS
Extended to 105 digits by Jean-François Alcover, Feb 05 2013
STATUS
approved