OFFSET
0,1
COMMENTS
gamma is A001620.
REFERENCES
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed., Academic Press, 2007, p. 656, 6.443.1.
LINKS
A. Erdélyi, ed., Tables of Integral Transforms, Vol. II, McGraw Hill, New York, 1954, p. 304, eq. (42).
Bakir Farhi, A curious formula related to the Euler Gamma function, arXiv:1312.7115 [math.NT], 2013.
Fábio M. S. Lima, Closed-form expressions for Farhi's constant and related integrals and its generalization, arXiv:1906.04303 [math.CA], 2019.
Niels Nielsen, Handbuch der Theorie der Gammafunktion, Teubner, Leipzig, 1906, p. 203, eq. (5).
Jean-Christophe Pain, Expression of Farhi's integral in terms of known mathematical constants, arXiv:2408.14835 [math.NT], 2024.
Michael Ian Shamos, Shamos's catalog of the real numbers, 2011, p. 414.
Zurab Silagadze, An integral related to the Euler gamma function, MathOverflow, 2014.
FORMULA
Equals Integral_{x=0..1} sin(2*Pi*x) log(Gamma(x)) dx.
EXAMPLE
0.38437394621343291560266431528895814385082767447477...
MAPLE
(log(2*Pi)+gamma)/2/Pi ; evalf(%) ;
MATHEMATICA
RealDigits[(Log[2*Pi] + EulerGamma) / (2*Pi), 10, 120][[1]] (* Amiram Eldar, Aug 19 2024 *)
PROG
(PARI) (log(2*Pi) + Euler)/(2*Pi) \\ Amiram Eldar, Sep 09 2024
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Aug 13 2024
STATUS
approved