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A210593 Decimal expansion of the series limit of sum_{k>=1} (-1)^k*log(k)/k^2. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..104.

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

Cf. A073002, A013661, A002162.

Sequence in context: A210602 A210801 A153091 * A179069 A235706 A124847

Adjacent sequences:  A210590 A210591 A210592 * A210594 A210595 A210596

KEYWORD

nonn,cons

AUTHOR

R. J. Mathar, Mar 23 2012

EXTENSIONS

Extended to 105 digits by Jean-François Alcover, Feb 05 2013

STATUS

approved

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Last modified May 29 07:29 EDT 2017. Contains 287243 sequences.