A225113 Decimal expansion of Integral_{x=0..1} arcsin(x)^2/x dx.

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

Offset

0,1

References

George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 122.

Links

Table of n, a(n) for n=0..99.

Chenli Li, Wenchang Chu, Improper integrals involving powers of Inverse Trigonometric and hyperbolic Functions, Mathematics 10 (16) (2022) 2980

D. Cvijovic, H. M. Srivastava, Evaluations of some classes of the trigonometric moment intgrals, J. Math. Anal. Applic. 351 (2009) 244-256, example set 1.

J. C. Tanner, The Proportion of Quadrilaterals Formed by Random Lines in a Plane, Journal of Applied Probability, Vol. 20, No. 2 (Jun., 1983), pp. 400-404.

J. C. Tanner, Polygons Formed by Random Lines in a Plane: Some Further Results, Journal of Applied Probability, Vol. 20, No. 4 (Dec., 1983), p. 778

Formula

Equals 1/8*(Pi^2*log(4) - 7*zeta(3)).

Also equals sum(n>=1, 4^(n-1)/(n^3*binomial(2*n, n)).

Also equals 1/2*hypergeometric4F3([1, 1, 1, 1], [3/2, 2, 2], 1).

Also equals Integral_{x=0..Pi/2} x^2*cot(x) dx. - Michel Marcus, Aug 29 2015

Example

0.65847232569963413648709889716600527590558175624904185726279535120517...

Mathematica

1/8*(Pi^2*Log[4] - 7*Zeta[3]) // RealDigits[#, 10, 100]& // First

Prog

(PARI) (Pi^2*log(4) - 7*zeta(3))/8 \\ Michel Marcus, Sep 04 2015

Crossrefs

Cf. A002117 (zeta(3)).

Sequence in context: A242759 A021607 A298172 * A329247 A133618 A194599

Adjacent sequences: A225110 A225111 A225112 * A225114 A225115 A225116

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 29 2013

Status

approved