A375368 - OEIS

%I #22 Jul 08 2026 09:04:20

%S 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,

%T 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,

%U 9,8,1,4,9,6,3,7,1,9,6,9,2,7,5,4,5,1,3,2,1

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

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

%H Olivier Espinosa and Victor H. Moll, <a href="https://dx.doi.org/10.1023/A:1015706300169">On some integrals involving the Hurwitz zeta function: Part 1</a>, Raman. J. 6 (2002) 159-188, Example 6.4.

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

%F Equals log(A367842). - _Hugo Pfoertner_, Aug 19 2024

%e 0.21071478956855210834291187462669484383332902315035...

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

%t RealDigits[Zeta'[2] / (2*Pi^2) + Log[2*Pi] / 6 - EulerGamma / 12, 10, 120][[1]] (* _Amiram Eldar_, Aug 19 2024 *)

%o (PARI) zeta'(2)/2/Pi^2 + log(2*Pi)/6 - Euler/12 \\ _Charles R Greathouse IV_, Jul 08 2026

%Y Cf. A001620, A073002, A367842, A375369.

%K nonn,cons,changed

%O 0,1

%A _R. J. Mathar_, Aug 13 2024