A098459 Decimal expansion of G/2 + (1/8)*Pi*log(2), where G is Catalan's constant (often also denoted K).

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

Offset: 0

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004

Keywords

• nonn
• cons
• easy

Examples

			0.7301810583765597738398878697...
		

References

• Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2004, p. 20.

Links

• Eric Weisstein's World of Mathematics, Ahmed's Integral

Crossrefs

Cf. A006752, A102886, A096615, A102521.

Programs

Mathematica

RealDigits[Catalan/2 + Pi*Log[2]/8, 10 , 100][[1]] (* Amiram Eldar, Aug 17 2020 *)

Formula

Equals Integral_{x=0..1} arctan(x) / (x*(x^2+1)) dx.

From Amiram Eldar, Aug 17 2020: (Start)

Equals (1/2) * A006752 + A102886.

Equals Integral_{x=0..Pi/4} x*cot(x) dx. (End)