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
G. C. Greubel, Table of n, a(n) for n = 0..10000
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.
Wikipedia, Dirichlet eta function
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
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Mar 23 2012
EXTENSIONS
Extended to 105 digits by Jean-François Alcover, Feb 05 2013
STATUS
approved