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%I #31 Jan 02 2023 03:24:58
%S 3,2,3,3,6,7,4,3,1,6,7,7,7,7,8,7,6,1,3,9,9,3,7,0,0,8,7,9,5,2,1,7,0,4,
%T 4,6,6,5,1,0,4,6,6,2,5,7,2,5,4,6,9,6,6,1,6,8,1,0,3,6,4,4,3,4,3,1,7,9,
%U 0,3,3,7,2,1,0,6,7,2,8,9,4,4,3,1,9,3,0,3,7,0,4,6,4,1,0,2,4,5,1,3,8,0,2,8,0
%N Decimal expansion of Integral_{x=0..1} cos((log x)/x)/x dx.
%C Decimal expansion of solution to problem #1 in the Trefethen challenge.
%C Conjecturally, the value of the Borel sum of the divergent series Sum_{n >= 1} (-1)^(n+1)*(2*n)^(2*n-1). See Finch, p. 62. - _Peter Bala_, Dec 28 2022
%H Amiram Eldar, <a href="/A117231/b117231.txt">Table of n, a(n) for n = 0..10001</a> (from Dirk Laurie's solution)
%H Folkmar Bornemann, <a href="http://www-m3.ma.tum.de/foswiki/pub/M3/Allgemeines/FolkmarBornemannPublications/short.pdf">Short remarks on the solution of the SIAM 100-digit challenge</a>, 2002.
%H Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/">The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing</a>, SIAM, Philadelphia, 2004.
%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2022.
%H Walter Gautschi, <a href="http://dx.doi.org/10.1007/s11075-008-9157-z">The numerical evaluation of a challenging integral</a>, Num. Alg. 49 (1-4) (2008) 187-194.
%H Dirk Laurie, <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/Chapter1/">A Twisted Tail</a>, a web page for the book The SIAM 100-Digit Challenge.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hundred-DollarHundred-DigitChallengeProblems.html">Hundred-Dollar, Hundred-Digit Challenge Problems</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hundred-dollar,_Hundred-digit_Challenge_problems">Hundred-dollar, Hundred-digit Challenge problems</a>.
%e Integral_{t = 0..1} t^(-1)*cos(t^(-1)*log(t)) dt = 0.32336743167777876139937..
%t RealDigits[ NIntegrate[ ProductLog'[u]*Cos[u], {u, 0, Infinity}, WorkingPrecision -> 220]][[1]][[1 ;; 105]] (* _Jean-François Alcover_, Oct 26 2012, after W. Gautschi *)
%Y Cf. A117232, A117233, A117234, A117235, A117236, A117237, A117238, A117239, A117240.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Mar 05 2006
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