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A094720 Fill's first logarithmic constant. 2

%I

%S 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,

%T 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,

%U 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

%N Fill's first logarithmic constant.

%H J. A. Fill, Ph. Flajolet and N. Kapur, <a href="http://arXiv.org/abs/math.CO/0306225">Singularity analysis, Hadamard products and tree recurrences</a>

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

%e 1.2035649167496103342...

%t RealDigits[ -EulerGamma - 2*NIntegrate[((t - 2)*Log[1 - t] - 2*t)*(Log[Log[1/t]]/t^3), {t, 0, 1},

%t WorkingPrecision -> 170, MaxRecursion -> 20]][[1]][[;; 105]] (* _Jean-Fran├žois Alcover_, Jun 30 2011 *)

%Y Cf. A094721.

%K nonn,cons

%O 1,2

%A _Ralf Stephan_, May 25 2004

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

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Last modified October 25 17:22 EDT 2021. Contains 348255 sequences. (Running on oeis4.)