A119806 Decimal expansion of cos(gamma).

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

Offset

0,1

Comments

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)?

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

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.

Toyesh Prakash Sharma, The Applications of the Stirling's approximation to find limits, Revista Electronica MateInfo.ro, December 2020, pp. 44-49. See Problem 4, p. 46.

Formula

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

Example

0.8379852878801965399549928612589497248086592013241766579...

Mathematica

RealDigits[Cos[EulerGamma], 10, 150][[1]]

Prog

(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

Crossrefs

Cf. A001620 (Euler-Mascheroni constant), A073004, A119807.

Sequence in context: A099284 A061444 A011214 * A248296 A217732 A089260

Adjacent sequences: A119803 A119804 A119805 * A119807 A119808 A119809

Keyword

cons,nonn

Author

T. D. Noe, May 24 2006

Status

approved