A354683 - OEIS

%I #5 Jun 03 2022 05:35:31

%S 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,

%T 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,

%U 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

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

%C 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).

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

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

%H P. J. Schweitzer, <a href="https://www.jstor.org/stable/2029332">Problem 77-3, A Definite Integral of N. Bohr</a>, SIAM Review, Vol. 19, No. 1 (1977), p. 147; <a href="https://www.jstor.org/stable/2030159">Solution</a> by D. E. Amos, ibid., Vol. 20, No. 1 (1978), pp. 188-190.

%F 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.

%e -1.15063007089458760834881995377084891775092151763321...

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

%Y Cf. A000796, A001620, A002162.

%K nonn,cons

%O 1,3

%A _Amiram Eldar_, Jun 03 2022