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%I #35 Jul 25 2021 02:36:38
%S 4,2,0,1,9,5,0,5,8,2,5,3,6,8,9,6,1,7,2,5,7,9,8,3,8,4,0,3,7,9,0,2,0,3,
%T 7,1,2,4,5,3,8,9,2,0,5,5,7,0,3,4,4,1,7,6,9,9,5,6,8,8,8,9,9,6,8,5,6,8,
%U 9,8,9,9,1,5,7,2,4,7,7,1,3,4,1,1,4,6,2,9,4,7,2,7,4,6,8,4,4,6,0,4
%N Decimal expansion of -log(2-2*cos(1))/2.
%C From _Bernard Schott_, Apr 20 2021: (Start)
%C The series Sum_{k>=1} cos(k)/k and also Sum_{k>=1} sin(k)/k (A096444) are called Fresnel series.
%C Abel summation shows these two series are convergent.
%C The series Sum_{k>=1} |cos(k)/k| is divergent. (End)
%D Xavier Merlin, Methodix Analyse, Ellipses, 1997, p. 117.
%H Université de Rennes, <a href="http://braise.univ-rennes1.fr/donnees/ParamHTML/S%E9ries%20num%E9riques/con/S%E9ries%20semi-convergentes/cst.pdf">Séries semi-convergentes</a>, Base raisonnée d'exercices de Mathématiques, p. 2 (Braise).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Summation_by_parts">Summation by parts</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F Equals Sum_{k>=1} cos(k)/k.
%F Equals -log(2*sin(1/2)). - _Jianing Song_, Nov 09 2019
%F Equals log(csc(1/2)/2). - _Peter Luschny_, Apr 04 2020
%e 0.0420195058253689...
%t RealDigits[N[ -Log[2 - 2 Cos[1]]/2, 101]]
%o (PARI) -log(2-2*cos(1))/2 \\ _Charles R Greathouse IV_, May 15 2019
%Y Cf. A049470, A096444, A308573.
%K cons,nonn
%O -1,1
%A _Fredrik Johansson_, Aug 20 2006
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