A242011 - OEIS

%I #13 Jan 17 2020 05:39:03

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

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

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

%N Decimal expansion of sum_{k>=0} (-1)^k*(log(4k+1)/(4k+1)+log(4k+3)/(4k+3)).

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 8.

%F (Pi/(2*sqrt(3)))*(log(Gamma(1/8)/Gamma(3/8)/(Gamma(5/8)/Gamma(7/8))) - (gamma + log(2*Pi))), where gamma is Euler's constant and Gamma(x) is the Euler Gamma function.

%e 0.02300458786273601031799260214514696231866764147508832909638...

%t s = (Pi/(2*Sqrt[2]))*(Log[Gamma[1/8]*Gamma[3/8]/(Gamma[5/8]*Gamma[7/8])] - (EulerGamma + Log[2*Pi])); Join[{0}, RealDigits[s, 10, 99] // First]

%Y Cf. A203142, A203143, A203144, A203146.

%K nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Aug 11 2014