A357597 - OEIS

%I #69 Feb 26 2023 15:57:02

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

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

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

%N Decimal expansion of real part of zeta'(0, 1-sqrt(2)).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HurwitzZetaFunction.html">Hurwitz Zeta Function</a>, formula 16

%F Equals arcsinh(1) + log(Pi/2)/2 + log(-csc(Pi*sqrt(2))/Gamma(sqrt(2)-1)).

%F Equals Re(log(Gamma(1-sqrt(2))/sqrt(2*Pi))).

%F Equals log(-sqrt(Pi)/(sqrt(2)!*sin(sqrt(2)*Pi))). - _Peter Luschny_, Feb 26 2023

%e 0.38293875264914751259357185...

%p Re(evalf(Zeta(1, 0, 1 - sqrt(2)), 120)); # _Vaclav Kotesovec_, Feb 26 2023

%t RealDigits[N[ArcSinh[1] + Log[Pi/2]/2 + Log[-Csc[Sqrt[2] Pi]/Gamma[Sqrt[2] - 1]], 105]][[1]]

%o (PARI) real(zetahurwitz'(0, 1-sqrt(2))) \\ _Vaclav Kotesovec_, Feb 26 2023

%Y Cf. A324995, A324996.

%K cons,nonn

%O 0,1

%A _Artur Jasinski_, Feb 25 2023