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 A094691 Decimal expansion of -Integral_{x=0..1} (Sqrt(x)/Log(1-x)) dx. 1

%I

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

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

%U 3,8,5,5,4,8,3,8,7,5,0,4,5,8,8,3,7,9,3,0,6,8

%N Decimal expansion of -Integral_{x=0..1} (Sqrt(x)/Log(1-x)) dx.

%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap103.html">-int(sqrt(x)/log(1-x),x=0..1)</a>.

%F Also equals 5/3 - 2*sum(abs(sum((BernoulliB(j)*StirlingS1(k, j-1))/j, {j, 1, k+1}))/((2*k+3)*k!), k=1..infinity}). [_Jean-François Alcover_, Apr 12 2013]

%e 1.601402243549887613933249892371286056672410899314165453273114871045738554838...

%t -NIntegrate[ Sqrt[x]/Log[1 - x], {x, 0, 1}, MaxRecursion -> 24, WorkingPrecision -> 98]

%t RealDigits[NIntegrate[Sqrt[x]/Log[1-x],{x,0,1},WorkingPrecision-> 120],10,120] [[1]] (* _Harvey P. Dale_, Apr 05 2019 *)

%K cons,nonn

%O 1,2

%A _Robert G. Wilson v_, May 19 2004

%E Corrected and extended by _Harvey P. Dale_, Apr 05 2019

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Last modified December 7 20:44 EST 2019. Contains 329849 sequences. (Running on oeis4.)