A354683 Decimal expansion of -2 - (1 - gamma - log(2))*Pi (negated).

1, 1, 5, 0, 6, 3, 0, 0, 7, 0, 8, 9, 4, 5, 8, 7, 6, 0, 8, 3, 4, 8, 8, 1, 9, 9, 5, 3, 7, 7, 0, 8, 4, 8, 9, 1, 7, 7, 5, 0, 9, 2, 1, 5, 1, 7, 6, 3, 3, 2, 1, 8, 7, 1, 8, 0, 1, 3, 0, 0, 1, 2, 6, 0, 9, 1, 5, 9, 9, 8, 6, 2, 7, 4, 7, 9, 4, 2, 4, 9, 7, 3, 5, 5, 2, 3, 6, 0, 3, 5, 9, 8, 5, 9, 9, 0, 3, 6, 0, 1, 7, 8, 5, 4, 3

Offset

1,3

Comments

The value of the integral given in the Formula section. It was discussed by Niels Bohr in a letter to his brother, Harald (June 12, 1912).

References

Niels Bohr, Collected Works, Vol. I, L. Rosenfeld, ed., North-Holland, Amsterdam, 1972, pp. 554-557.

Murray S. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM Review, Philadelphia, 1987, pp. 252-253.

Links

Table of n, a(n) for n=1..105.

P. J. Schweitzer, Problem 77-3, A Definite Integral of N. Bohr, SIAM Review, Vol. 19, No. 1 (1977), p. 147; Solution by D. E. Amos, ibid., Vol. 20, No. 1 (1978), pp. 188-190.

Formula

Equals Integral_{x=-oo..oo} F(x)*(F'(x)-log(x)) dx, where F(x) = Integral_{y=-oo..oo} cos(x*y)/(1+y^2)^(3/2) dy.

Example

-1.15063007089458760834881995377084891775092151763321...

Mathematica

RealDigits[-2 - (1 - EulerGamma - Log[2]) * Pi, 10, 100][[1]]

Crossrefs

Cf. A000796, A001620, A002162.

Sequence in context: A197030 A035550 A197508 * A159751 A190914 A153458

Adjacent sequences: A354680 A354681 A354682 * A354684 A354685 A354686

Keyword

nonn,cons

Author

Amiram Eldar, Jun 03 2022

Status

approved