A093753 Decimal expansion of (-2*Catalan + Pi*log(2))/2.

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

Offset: 0

Author

Eric W. Weisstein, Apr 15 2004

Keywords

• nonn
• cons

Examples

			0.17282745097458205019574...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.7.2, p. 55.

Links

• Su Hu, Min-soo Kim, Euler's integral, multiple cosine function and zeta values, arXiv:2201.011247 (2023), Example 2.5.
• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 215.
• Eric Weisstein's World of Mathematics, Radial Integrals.

Crossrefs

Cf. A001008, A002805, A006752, A093754, A173623.

Programs

Maple

evalf(-Catalan+Pi*log(2)/2) ; # R. J. Mathar, Apr 01 2010

Mathematica

First[RealDigits[Pi*Log[2]/2 - Catalan, 10, 100]] (* Paolo Xausa, Apr 27 2024 *)

PARI

Pi*log(2)/2 - Catalan \\ Michel Marcus, Sep 22 2014

Formula

Equals Integral_{x=0..1; y=0..1} [x^2+y^2>1]/(x^2+y^2) where [] is the Iverson bracket.

Equals Integral_{0..1} log(1+x^2)/(1+x^2) dx. - Jean-François Alcover, Sep 22 2014

Equals Sum_{k>=1} (-1)^(k+1) * H(k)/(2*k+1), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, Jul 22 2020