OFFSET
1,2
LINKS
Simon Plouffe, -int(sqrt(x)/log(1-x),x=0..1).
FORMULA
Equals 5/3 - 2*Sum_(abs(Sum_((BernoulliB(j)*Stirling1(k, j-1))/j, {j, 1, k+1}))/((2*k+3)*k!), k=1..infinity}). [Jean-François Alcover, Apr 12 2013]
Equals Integral_{x=0..1} beta(x+1,1/2) dx. - Jean-Luc Marichal, Sep 22 2020
EXAMPLE
1.601402243549887613933249892371286056672410899314165453273114871045738554838...
MATHEMATICA
-NIntegrate[ Sqrt[x]/Log[1 - x], {x, 0, 1}, MaxRecursion -> 24, WorkingPrecision -> 98]
RealDigits[NIntegrate[Sqrt[x]/Log[1-x], {x, 0, 1}, WorkingPrecision-> 120], 10, 120] [[1]] (* Harvey P. Dale, Apr 05 2019 *)
PROG
(PARI) -intnum(x=0, 1, sqrt(x)/log(1-x)) \\ Michel Marcus, Sep 23 2020
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, May 19 2004
EXTENSIONS
Corrected and extended by Harvey P. Dale, Apr 05 2019
STATUS
approved