OFFSET
0,1
COMMENTS
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.
REFERENCES
Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année, MP, Dunod, 1997, Exercice 3.3.2.j page 283.
FORMULA
Equals Sum_{n>=0} log(cos(1/2^n)).
EXAMPLE
-0.7882302166551059406604484922728009...
MAPLE
evalf(sum(ln(cos(1/2^n)), n=0..infinity), 110);
MATHEMATICA
RealDigits[Log[Sin[2]/2], 10, 100][[1]] (* Amiram Eldar, May 08 2022 *)
PROG
(PARI) log(sin(2)/2) \\ Michel Marcus, May 08 2022
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, May 08 2022
STATUS
approved