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A369884 Decimal expansion of - Integral_{x=0..1} log(1 - x)/(x^2 + x) dx.

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%I A369884 #16 Aug 05 2024 13:34:06
%S A369884 1,0,6,2,6,9,3,5,4,0,3,8,3,2,1,3,9,3,0,5,6,9,7,5,8,8,4,6,4,8,6,3,4,5,
%T A369884 0,8,0,4,7,4,7,5,1,4,2,6,4,0,0,6,7,2,0,1,2,3,0,1,2,1,1,1,8,1,4,9,6,8,
%U A369884 3,6,4,2,6,3,3,1,5,1,7,6,7,3,0,1,6,7,8,8,5,8,2,0,3,1,8,4,2,8,4,8,1,1,8,3,5,9,9
%N A369884 Decimal expansion of - Integral_{x=0..1} log(1 - x)/(x^2 + x) dx.
%H A369884 R. Barbieri, J. A. Mignaco and E. Remiddi, <a href="https://dx.doi.org/10.1007/BF02728545">Electron form factors up to fourth order. I.</a>, Il Nuovo Cim. 11A (4) (1972) 824-864, Table I (8).
%H A369884 Michael Ian Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">A catalog of the real numbers</a> (2011), p. 110.
%H A369884 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%H A369884 Wikipedia, <a href="https://en.wikipedia.org/wiki/Harmonic_number">Harmonic number</a>.
%F A369884 Equals - Integral_{x=0..1} log(1 - x)/(x^2 + x) dx.
%F A369884 Equals Pi^2/12 + log(2)^2/2 [Shamos].
%F A369884 Equals Sum_{k=>1} H(k)^2/2^(k + 1), where H(k) is the k-th Harmonic number [Shamos].
%F A369884 Equals (Pi^2/6 + log(2)^2)/2 = A348373/2
%e A369884 1.062693540383213930569758846486345080474751426...
%t A369884 RealDigits[Pi^2/12 + Log[2]^2/2, 10, 120][[1]] (* _Amiram Eldar_, Feb 04 2024 *)
%o A369884 (PARI) - intnum(x=0,1,log(1-x)/(x^2+x))
%Y A369884 Cf. A000796, A002162, A001008, A002805, A348373.
%K A369884 nonn,cons
%O A369884 1,3
%A A369884 _Claude H. R. Dequatre_, Feb 04 2024