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A219705 Decimal expansion of cos(log(2)). 2


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

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

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

%N Decimal expansion of cos(log(2)).

%C In a letter to Christian Goldbach dated December 9, 1741, Leonhard Euler gave 10/13 as a rational approximation of this number.

%C Also, real part of 2^i. - _Bruno Berselli_, Dec 31 2012

%C The imaginary part of 2^i is A220085. - _Robert G. Wilson v_, Feb 04 2013

%D W. Michael Kelley, The Humongous Book of Calculus Problems. New York: Alpha Books (Penguin Group) p. 233, Problem 15.22.

%H Paul J. Nahin, <a href="http://press.princeton.edu/titles/9259.html">An Imaginary Tale: The Story of sqrt(-1)</a>, Princeton, New Jersey: Princeton University Press (1988), 143 - 144.

%H Elizabeth Volz, <a href="http://www.rowan.edu/colleges/csm/departments/math/facultystaff/nguyen/euler/translations/Euler%20Goldbach%20Letters%20Complex%20Exponential%20Paradox%20English%20Translation.pdf">An English translation of portions of seven correspondences between Euler and Goldbach on Euler’s complex exponential paradox and special values of cosine</a>, 2008

%H Elizabeth Volz and Hieu D. Nguyen, <a href="http://www.rowan.edu/colleges/csm/departments/math/facultystaff/nguyen/euler/articles/Euler%20Goldbach%20and%20Exact%20Values%20of%20Trigonometric%20Functions.pdf">Euler, Goldbach and exact values of trigonometric functions</a>, 2008 preprint

%F cos(log(2)) = (2^i + 2^(-i))/2.

%e 0.76923890136...

%t RealDigits[Cos[Log[2]], 10, 105][[1]]

%o (PARI) cos(log(2)) \\ _Charles R Greathouse IV_, Nov 25 2012

%o (Maxima) fpprec:110; ev(bfloat(cos(log(2)))); /* _Bruno Berselli_, Dec 31 2012 */

%Y Cf. A002162, A021017, A220085 (imaginary part of 2^i).

%K nonn,cons

%O 0,1

%A _Alonso del Arte_, Nov 25 2012

%E a(43) ff. corrected by _Georg Fischer_, Apr 03 2020

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Last modified July 25 16:03 EDT 2021. Contains 346291 sequences. (Running on oeis4.)