A375368 Decimal expansion of zeta'(2)/(2*Pi^2) + log(2*Pi)/6 - gamma/12.

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

Offset: 0

Author

R. J. Mathar, Aug 13 2024

Keywords

• nonn
• cons

Comments

zeta'(2) = -0.9375.. is the first derivative of the zeta function (see A073002). Gamma is A001620.

Examples

			0.21071478956855210834291187462669484383332902315035...
		

Links

• Olivier Espinosa and Victor H. Moll, On some integrals involving the Hurwitz zeta function: Part 1, Raman. J. 6 (2002) 159-188, Example 6.4.

Crossrefs

Cf. A001620, A073002, A367842, A375369.

Programs

Maple

Zeta(1,2)/2/Pi^2+log(2*Pi)/6-gamma/12 ; evalf(%) ;

Mathematica

RealDigits[Zeta'[2] / (2*Pi^2) + Log[2*Pi] / 6 - EulerGamma / 12, 10, 120][[1]] (* Amiram Eldar, Aug 19 2024 *)

Formula

Equals Integral_{x=0..1} x* log(Gamma(x)) dx.

Equals log(A367842). - Hugo Pfoertner, Aug 19 2024