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A347166
Decimal expansion of (gamma + log(2)) * Pi / 2.
0
1, 9, 9, 5, 4, 8, 1, 2, 9, 1, 3, 4, 7, 6, 0, 2, 8, 1, 5, 0, 5, 6, 9, 1, 1, 7, 1, 4, 7, 5, 4, 3, 2, 6, 9, 8, 3, 2, 2, 3, 1, 2, 3, 9, 4, 0, 8, 7, 0, 9, 4, 3, 5, 5, 1, 4, 8, 0, 9, 7, 1, 6, 6, 5, 6, 9, 5, 9, 0, 8, 8, 8, 9, 4, 0, 3, 3, 9, 2, 0, 1, 2, 5, 3, 7, 8, 3
OFFSET
1,2
COMMENTS
Shamos has incorrect integral expression for this constant.
REFERENCES
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press (1979), Eq. (4.421.1).
FORMULA
Equals -Integral_{x=0..infinity} log(x) * sin(2*x) / x dx.
More generally, Integral_{x=0..infinity} log(x) * sin(k*x) / x dx = -(Pi/2) * (gamma+log(k)).
EXAMPLE
1.995481291347602815056911714754326983223123940...
MAPLE
evalf((gamma+log(2))*Pi/2, 140); # Alois P. Heinz, Aug 20 2021
MATHEMATICA
RealDigits[(EulerGamma + Log[2])*Pi/2, 10, 120][[1]] (* Amiram Eldar, Jun 07 2023 *)
PROG
(PARI) (Euler + log(2))*Pi/2 \\ Michel Marcus, Aug 20 2021
CROSSREFS
Cf. A001620.
Sequence in context: A347151 A229191 A376642 * A347081 A347152 A131744
KEYWORD
nonn,cons
AUTHOR
Sean A. Irvine, Aug 20 2021
STATUS
approved