A244928 Decimal expansion of Ti_2(2-sqrt(3)), where Ti_2 is the inverse tangent integral function.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.7.6 Inverse Tangent Integral, p. 57.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

E. D. Krupnikov, K. S. Kölbig, Some special cases of the generalized hypergeometric function (q+1)Fq, J. Comp. Appl. Math. 78 (1997) 79-95.

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 304.

Eric Weisstein's MathWorld, Inverse Tangent Integral.

Eric Weisstein's MathWorld, Polylogarithm.

Formula

2/3*G + Pi/12*log(2-Sqrt(3)), where G is Catalan's number.

Also equals i/2*(polylog(2, -i*(2-sqrt(3))) - polylog(2, i*(2-sqrt(3)))), with i = sqrt(-1).

Equals 3F2(1/2,1,1; 3/2,3/2 ; 1/4)/4 [Krupnikov] - R. J. Mathar, May 13 2024

Example

0.26586495827930698269187508639712068764278382397513899938059741532857439513...

Mathematica

2/3*Catalan + Pi/12*Log[2 - Sqrt[3]] // RealDigits[#, 10, 105]& // First

Prog

(PARI) default(realprecision, 100); (2/3)*Catalan + Pi/12*log(2 - sqrt(3)) \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); (2/3)*Catalan(R) + Pi(R)/12*Log(2 - Sqrt(3)); // G. C. Greubel, Aug 25 2018

Crossrefs

Cf. A006752, A244929.

Sequence in context: A199159 A175293 A021083 * A319016 A262096 A011043

Adjacent sequences: A244925 A244926 A244927 * A244929 A244930 A244931

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 08 2014

Status

approved