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%I #16 Apr 02 2022 09:23:30
%S 8,3,7,9,8,5,2,8,7,8,8,0,1,9,6,5,3,9,9,5,4,9,9,2,8,6,1,2,5,8,9,4,9,7,
%T 2,4,8,0,8,6,5,9,2,0,1,3,2,4,1,7,6,6,5,7,9,0,4,1,1,7,8,9,3,5,5,6,7,7,
%U 6,9,3,6,8,8,8,0,2,6,2,2,2,3,2,7,5,4,9,4,1,4,6,8,6,5,4,2,1,9,1,7,5,6,8,2,3
%N Decimal expansion of cos(gamma).
%C This is the real part of exp(i*gamma), where gamma is the Euler-Mascheroni constant A001620. See A119807 for the imaginary part. The constant exp(gamma) (A073004) appears in many formulas. Does exp(i*gamma)?
%H G. C. Greubel, <a href="/A119806/b119806.txt">Table of n, a(n) for n = 0..10000</a>
%H D. M. Bătineţu-Giurgiu and Neculai Stanciu, <a href="http://www.ssmrmh.ro/wp-content/uploads/2021/04/RMM-30-FINAL_compressed.pdf">Problem UP.328</a>, Romanian Mathematical Magazine, Vol. 30, Autumn edition (2021), p. 114; <a href="http://www.ssmrmh.ro/wp-content/uploads/2020/04/SOLUTION-UP328.pdf">Solutions</a>, by Mokhtar Khassani-Mostaganem and Marian Ursărescu.
%H D. M. Bătineţu-Giurgiu, Neculai Stanciu, and José Luis Díaz-Barrero, <a href="http://amj-math.com/wp-content/uploads/2020/07/AMJ2020-vol7iss1.pdf">The Last Three Decades of Lalescu Limit</a>, Arhimede Mathematical Journal, Vol. 7, No. 1 (2020), pp. 16-26. See Problem 7, pp. 23-24.
%H Toyesh Prakash Sharma, <a href="https://www.mateinfo.ro/reviste-de-matematica/revista-electronica-de-matematica-mateinfo-ro-aparitie-lunara-2065-6432/revista-mateinfo-ro/revista-electronica-mateinfo-ro-2020/1157-revista-electronica-mateinfo-ro-decembrie-2020">The Applications of the Stirling's approximation to find limits</a>, Revista Electronica MateInfo.ro, December 2020, pp. 44-49. See Problem 4, p. 46.
%F Equals 2 * e * lim_{n->oo) (sin(gamma(n))-sin(gamma))*(n!)^(1/n), where gamma(n) = Sum_{k=1..n} 1/k - log(n) (Bătineţu-Giurgiu, 2021). - _Amiram Eldar_, Apr 02 2022
%e 0.8379852878801965399549928612589497248086592013241766579...
%t RealDigits[Cos[EulerGamma],10,150][[1]]
%o (PARI) default(realprecision, 100); cos(Euler) \\ _G. C. Greubel_, Aug 30 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Cos(EulerGamma(R)) // _G. C. Greubel_, Aug 30 2018
%Y Cf. A001620 (Euler-Mascheroni constant), A073004, A119807.
%K cons,nonn
%O 0,1
%A _T. D. Noe_, May 24 2006
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