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Decimal expansion of log(sin(2)/2) (negated).
0

%I #18 May 09 2022 10:32:50

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

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

%U 9,7,5,6,7,0,7,6,7,2,6,5,3,5,8,1,5,0,9,6,3,7,6,1,9,6

%N Decimal expansion of log(sin(2)/2) (negated).

%C We have Sum_{n>=0} log(cos(a/2^n)) = log((sin(2*a))/(2*a)) for 0 < a < Pi/2; this is the particular case a = 1.

%D Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année, MP, Dunod, 1997, Exercice 3.3.2.j page 283.

%F Equals Sum_{n>=0} log(cos(1/2^n)).

%e -0.7882302166551059406604484922728009...

%p evalf(sum(ln(cos(1/2^n)),n=0..infinity),110);

%t RealDigits[Log[Sin[2]/2], 10, 100][[1]] (* _Amiram Eldar_, May 08 2022 *)

%o (PARI) log(sin(2)/2) \\ _Michel Marcus_, May 08 2022

%Y Cf. A049469.

%K nonn,cons

%O 0,1

%A _Bernard Schott_, May 08 2022