A074758 - OEIS

%I #24 Feb 18 2021 05:11:12

%S 2,6,8,6,0,9,1,7,0,9,6,1,2,8,3,2,7,9,1,1,1,6,4,7,8,7,4,8,7,2,4,8,7,1,

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

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

%N Decimal expansion of zeta'(1/2)/zeta(1/2).

%D S. J. Patterson, "An introduction to the theory of the Riemann Zeta-function", Cambridge studies in advanced mathematics 14, p. 29.

%F Equals log(8*Pi)/2 + EulerGamma/2 + Pi/4 = 2.6860917...

%F Equals (1/2) * (log(Pi) - Gamma'(1/4) / Gamma(1/4)). - _Mats Granvik_, Jul 30 2017

%e 2.686091709612832791116478748724871144507269625811776921584451315495547282857339...

%t RealDigits[Zeta'[1/2]/Zeta[1/2], 10, 120][[1]] (* _Vaclav Kotesovec_, Feb 18 2021 *)

%o (PARI) log(8*Pi)/2 + Euler/2 + Pi/4 \\ _Michel Marcus_, Jul 30 2017

%Y Cf. A059750.

%K cons,nonn

%O 1,1

%A _Benoit Cloitre_, Sep 28 2002