A261830 - OEIS

%I #7 Apr 18 2016 12:15:25

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

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

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

%N Decimal expansion of Integral_{0..1/2} log(gamma(x+1)) dx (negated).

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

%F -1/2-(7/24)*log(2)+(1/4)*log(Pi)+(3/2)*log(A), where A is the Glaisher-Kinkelin constant 1.282427... (A074962).

%e -0.042853740650290944556623040556199190297475932123443880740342442...

%t Join[{0}, RealDigits[-1/2 - (7/24)*Log[2] + (1/4)*Log[Pi] + (3/2) * Log[Glaisher], 10, 102] // First]

%o (PARI) -intnum(x=1,3/2,lngamma(x)) \\ _Charles R Greathouse IV_, Apr 18 2016

%Y Cf. A074962.

%K nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Sep 02 2015