A357597 Decimal expansion of real part of zeta'(0, 1-sqrt(2)).

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, 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, 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

Offset: 0

Author

Artur Jasinski, Feb 25 2023

Keywords

• cons
• nonn

Examples

			0.38293875264914751259357185...
		

Links

• Eric Weisstein's World of Mathematics, Hurwitz Zeta Function, formula 16

Crossrefs

Cf. A324995, A324996.

Programs

Maple

Re(evalf(Zeta(1, 0, 1 - sqrt(2)), 120)); # Vaclav Kotesovec, Feb 26 2023

Mathematica

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

PARI

real(zetahurwitz'(0, 1-sqrt(2))) \\ Vaclav Kotesovec, Feb 26 2023

Formula

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

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

Equals log(-sqrt(Pi)/(sqrt(2)!*sin(sqrt(2)*Pi))). - Peter Luschny, Feb 26 2023