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A119806
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Decimal expansion of cos(gamma).
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3
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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, 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, 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
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OFFSET
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0,1
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COMMENTS
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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)?
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LINKS
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D. M. Bătineţu-Giurgiu and Neculai Stanciu, Problem UP.328, Romanian Mathematical Magazine, Vol. 30, Autumn edition (2021), p. 114; Solutions, by Mokhtar Khassani-Mostaganem and Marian Ursărescu.
D. M. Bătineţu-Giurgiu, Neculai Stanciu, and José Luis Díaz-Barrero, The Last Three Decades of Lalescu Limit, Arhimede Mathematical Journal, Vol. 7, No. 1 (2020), pp. 16-26. See Problem 7, pp. 23-24.
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FORMULA
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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
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EXAMPLE
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0.8379852878801965399549928612589497248086592013241766579...
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MATHEMATICA
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RealDigits[Cos[EulerGamma], 10, 150][[1]]
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PROG
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(PARI) default(realprecision, 100); cos(Euler) \\ G. C. Greubel, Aug 30 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Cos(EulerGamma(R)) // G. C. Greubel, Aug 30 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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