A094720 Fill's first logarithmic constant.

1, 2, 0, 3, 5, 6, 4, 9, 1, 6, 7, 4, 9, 6, 1, 0, 3, 3, 4, 2, 8, 6, 2, 8, 3, 3, 3, 8, 1, 4, 8, 7, 3, 1, 3, 1, 7, 7, 5, 5, 5, 2, 8, 3, 8, 5, 7, 7, 0, 9, 6, 0, 7, 4, 0, 3, 9, 0, 3, 8, 2, 4, 2, 7, 8, 1, 0, 9, 4, 2, 0, 5, 9, 6, 0, 6, 5, 9, 9, 6, 1, 4, 0, 3, 4, 1, 9, 8, 1, 9, 2, 3, 0, 9, 4, 4, 4, 9, 2, 8, 9, 3, 7, 1, 4

Offset

1,2

Links

Table of n, a(n) for n=1..105.

J. A. Fill, Ph. Flajolet and N. Kapur, Singularity analysis, Hadamard products and tree recurrences

Formula

-gamma-2*integral(t=0..1, ((t-2)*log(1-t)-2*t)*log(log(1/t))/t^3 ).

Example

1.2035649167496103342...

Mathematica

RealDigits[ -EulerGamma - 2*NIntegrate[((t - 2)*Log[1 - t] - 2*t)*(Log[Log[1/t]]/t^3), {t, 0, 1},
WorkingPrecision -> 170, MaxRecursion -> 20]][[1]][[;; 105]]  (* Jean-François Alcover, Jun 30 2011 *)

Crossrefs

Cf. A094721.

Sequence in context: A262946 A343932 A216440 * A334495 A155800 A276658

Adjacent sequences: A094717 A094718 A094719 * A094721 A094722 A094723

Keyword

nonn,cons

Author

Ralf Stephan, May 25 2004

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 01 2006

Status

approved