A347166 Decimal expansion of (gamma + log(2)) * Pi / 2.

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).

Links

Table of n, a(n) for n=1..87.

Michael I. Shamos, Shamos's catalog of the real numbers (2011).

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: A155995 A347151 A229191 * A347081 A347152 A131744

Adjacent sequences: A347163 A347164 A347165 * A347167 A347168 A347169

Keyword

nonn,cons

Author

Sean A. Irvine, Aug 20 2021

Status

approved