A261829 - OEIS

%I #14 Mar 25 2019 02:44:04

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

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

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

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

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 135.

%F Equals -Integral_{0..infinity} x*log(x)/(exp(2*Pi* x)-1) dx.

%F Equals 1/24 - log(A)/2, where A is the Glaisher-Kinkelin constant 1.282427... (A074962).

%e 0.08271057185022546460695983012139032138201819016760089183326...

%p evalf(-Zeta(1, -1)/2, 102); # _Peter Luschny_, Mar 24 2019

%t Join[{0}, RealDigits[1/24 - Log[Glaisher]/2, 10, 101] // First]

%o (PARI) -zeta'(-1)/2 \\ _Michel Marcus_, Mar 24 2019

%Y Cf. A074962.

%K nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Sep 02 2015

%E New name by _Peter Luschny_, Mar 24 2019