OFFSET
1,3
REFERENCES
Paul J. Nahin, Inside Interesting Integrals, Springer 2015, ISBN 978-1493912766.
LINKS
Su Hu and Min-Soo Kim, Euler's integral, multiple cosine function and zeta values, arXiv:2201.01124 [math.NT], 2022.
K. S. Kölbig, On the integral int_0^Pi/2 log^n cos x log^p sin x dx, Math. Comp. 40 (162) (1983) 565-570, r_{1,0}
Richard J. Mathar, Chebyshev approximation of x^m(-log x)^l in the interval 0 <= x <= 1, arXiv:2408.15212 [math.CA], 2024. See p. 2.
Kazuhiro Onodera, Generalized log sine integrals and the Mordell-Tornheim zeta values, Trans. Am. Math. Soc. 363 (3) (2010) 1463.
FORMULA
Equals abs(Integral {x=0..Pi/2} log(sin(x)) dx).
Equals A086054 / 2.
From Amiram Eldar, Jul 13 2020: (Start)
Equals Integral_{x=0..1} arcsin(x)/x dx.
Equals Integral_{x=0..Pi/2} x*cot(x) dx. (End)
Equals Integral_{x = 0..1} log(x + 1/x)/(1 + x^2) dx (Nahin, 2.4.4) = (1/2)*Integral_{x = 0..oo} log(x^2 + 4)/(x^2 + 4) dx = (1/2)*Integral_{x = 0..oo} log(x^2 + 1)/(x^2 + 1) dx = Integral_{x = 0..oo} log(x^2 + 64)/(x^2 + 64) dx. - Peter Bala, Jul 22 2022
Equals 3F2(1/2,1/2,1/2 ; 3/2,3/2 ; 1). - R. J. Mathar, Aug 19 2024
EXAMPLE
1.08879304515180106525034444...
MAPLE
Pi/2*log(2) ; evalf(%) ;
MATHEMATICA
RealDigits[Pi*Log[2]/2, 10, 100][[1]] (* Amiram Eldar, Jul 13 2020 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Nov 08 2010
STATUS
approved