OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Hurwitz Zeta Function, formula 16
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
EXAMPLE
0.38293875264914751259357185...
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]]
PROG
(PARI) real(zetahurwitz'(0, 1-sqrt(2))) \\ Vaclav Kotesovec, Feb 26 2023
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Artur Jasinski, Feb 25 2023
STATUS
approved