A173623 Decimal expansion of Pi*log(2)/2.

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

Offset

1,3

References

Paul J. Nahin, Inside Interesting Integrals, Springer 2015, ISBN 978-1493912766.

Links

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

Su Hu and Min-Soo Kim, Euler's integral, multiple cosine function and zeta values, arXiv:2201.01124 [math.NT], 2022.

K. 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 Sum_{k>=0} binomial(2*k,k)/(4^k*(2*k+1)^2) = Sum_{k>=0} A000984(k)/A164583(k).

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

Example

1.08879304515180106525034444...

Maple

Pi/2*log(2) ; evalf(%) ;

Mathematica

RealDigits[Pi*Log[2]/2, 10, 100][[1]] (* Amiram Eldar, Jul 13 2020 *)

Crossrefs

Cf. A000984, A086054, A164583.

Sequence in context: A127196 A350715 A294795 * A070481 A011109 A248622

Adjacent sequences: A173620 A173621 A173622 * A173624 A173625 A173626

Keyword

nonn,cons

Author

R. J. Mathar, Nov 08 2010

Status

approved