A377981 Decimal expansion of G/2 - Pi*log(2)/8, where G = A006752.

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

Offset: 0

Author

Stefano Spezia, Nov 13 2024

Keywords

• nonn
• cons

Examples

			0.18578453580065924121471564518649031196975172459...
		

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

• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 230.

Crossrefs

Cf. A006752, A102886.

Programs

Mathematica

RealDigits[Catalan/2-Pi Log[2]/8,10,100][[1]]

Formula

Equals Sum_{n>=0} (-1)^(n+1)/(2*n + 1) Sum_{k=0..n-1} 1/(2*k + 1) (see Finch).

Equals Integral_{x=0..Pi/4} x*tan(x) dx (see Shamos).

Equals A006752/2 - A102886.